Algebraic expressions for class 7

In previous classes, you were introduced to algebra. Now in class 7 algebraic expressions, you will read about algebraic expressions in more detail. Today, you will learn complete concepts with the help of examples,ncert solution, worksheet, and important and answer of problems which recently asked by students on this topic. So, if you have the same problem you can read or comment for any related query.

The basic of algebraic expression starts with the term “Constants” and “Variables”.

Constants: Constants are real numbers or numerical values that are significant.

Example: 10,20,240…..etc

Variables: A quantity that can change or vary taking on different numerical values is known as variables.

Example: 6+n,n,x….etc

Ratio and proportion for class 7 in detail 

Rational number for class 8 

Algebraic expressions for class 7

A combination of constants and variables connected by any symbols like +,-,×and ÷ is called an algebraic expression.

For examples : 2x+3y ,9x³ , 18a+13b ..etc

Terms of the expressions

A term in an algebraic expression is the constant and variables that form algebraic expressions.

Example: 8a-4b+11c is an algebraic expression in which 8a,-4b, and 11c are known as terms

Factors of a term

A term can be the product of two or more factors as given in the following examples

  1.  The term 8xy is a product of factors 8,x, and y. The factors of 8 are 8,x, and y.
  2. In the term -5abc ,the factors are -5 ,a,b and c .
Coefficient

Any factor of the term is called the coefficients of the products of the remaining factors. A coefficient may be a numerical factor or an algebraic factor or a product of two or more factors. Let’s take examples to understand it clearly

(i) In the expressions 3pq, number 3 is the numerical coefficient of pq ,p is the coefficient of 3q and q is the coefficient of 3p.

(ii) In x, the coefficient of x is 1.When no number is written before a letter, its numerical coefficients are understood to be 1.

constant term

The term of an algebraic expression having no literal factor is called a constant term. For example

(i) In the algebraic expressions 12x²+15y²-16, the constant term is -16.

(ii) In 8x²y-6z, as there is no constant term, we consider it as 0

Like term

Like terms are the terms having the same variables and equivalent powers. For example

  1. 2x²,3x²,-18x² are like terms
  2.  13ab²,24ab² are like terms
Unlike terms

Terms either not having the same variables or those with the same variables but the unequal powers are called, unlike terms.

Naming an algebraic expressions

Algebraic expressions is divided on the basis of “No of terms” and ” Powers”.

Algebraic expression are of 5 types on the basis of “No of terms”

Monomial: An algebraic expression containing only one term is called a monomial.

For example 15cd, 100 and a³b²c²

Binomial: An expression that contains two unlike terms is called a binomial. For example, 3m +4n,z²-9, and xy+5z.

Remember: Expression 3y+5y is not a binomial as its terms 3y and 7y are like terms

Trinomial: An expression which contains three unlike terms is called a trinomial

Example: a+b+c,x²+2x+1 and 1+a+y .

Quadrinomial: An expression that contains four unlike terms is called a quadrinomial.

For example: x+y+z+1,3m³+15m²+7m+4

Algebraic expressions for class 7 ncert solution

 Algebraic expressions for class 7 exercise 12.1

Q.1 Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations:

(i) Subtraction of z from y

(ii) One half of the sum of the numbers x and y

(iii) The number z is multiplied by itself

(iv) One -fourth of the products of numbers p and q

(v) Numbers x and y are both squared and added

(vi) Number 5 is added to the three times of product of number m and n

(vii) Products of number y and 2  is subtracted from 10

(viii)Sum of the number a and b subtracted from their product

Sol.(i) Subtraction of z from y

Algebraic expression=y-z

Sol.(ii) One half of the sum of the numbers x and y

Algebraic expression=\frac{1}{2}(x+y)

Sol(iii) The number z is multiplied by itself

Algebraic expression=z×z=z²

Sol(iv) One -fourth of the products of numbers p and q

Algebraic expression: \frac{1}{4}(pq)

Sol(v) Numbers x and y are both squared and added

Algebraic expression=x²+y²

Sol(vi)Number 5 is added to the three times of product of number m and n

Algebraic expression= 3mn+5

Sol(vii) Products of number y and 2  is subtracted from 10

Algebraic expression= 10-2y

Sol(viii) Sum of the number a and b subtracted from their product

Algebraic expression = ab-(a+b)=ab-a-b

Q.2(i) Identify the term and their factors in the following expression show the terms are and factors by tree diagrams

(a) x-3

(b) 1+x+x²

(c) y-y³

(d) 5xy²+7x²y

(e) -ab+2b²-3a²

(ii) Identify terms and factor in the expression given below

(a) -4x+5

(b) -4x+5y

(c) 5y+3y²

(d) xy+2x²y²

(e) pq+q

(f)1.2ab-2.4b+3.6a

(g) \frac{3}{4}x+\frac{1}{4}

(h) 0.1p²+0.2q²

Sol.

Algebraic expression                                          terms                      factors

(a)-4x+5                                                                  -4x                             -4×x

5                                5

(b)-4x+5y                                                               -4x                             -4×x

5y                                5×y

(c) 5y+3y²                                                               5y                                5×y

3y²                              3×y×y

(d)xy+2x²y²                                                          xy                                  x×y

2x²y²                             2×x×x×y×y

(e) pq+q                                                                pq                                   p×q

q                                       q

(f) )1.2ab-2.4b+3.6a                                        1.2ab                                   1.2×a×b

-2.4b                                    2.4×b

3.6a                                     3.6×a

(g) \frac{3}{4}x+\frac{1}{4} \frac{3}{4}x \frac{3}{4}×x

(h) 0.1p²+0.2q²                                              0.1p²                                     0.1×p×p

0.2q²                                   0.2 ×q×q

Q.3 Identify the numerical coefficients of the term (other than constant) in the following

(i) 5-3t²

(ii) 1+t+t²+t³

(iii) x+2xy+3y

(iv) 100m+1000n

(v) -p²q²+7pq

(vi) 1.2a+0.86

(vii) 3.14r²

(viii) 2(l+b)

(ix) 0.1y+0.01y²

Sol(i) 5-3t²

Here – 3 is the coefficient of t²

Sol(ii) 1+t+t²+t³

1 is the coefficient of t

1 is the coefficient of t²

1 is the coefficient of t³

Sol.(iii) x+2xy+3y

1 is the coefficent of x

2 is the coefficient of xy

3 is the coefficient of y

Sol(iv) 100m+1000n

100 is the coefficient of m

1000 is the coefficient of n

Sol.(v) -p²q²+7pq

-1 is the coefficient of p²q²

7 is the coefficient of pq

Sol.(vi)1.2a+0.86

1.2 is the coefficient of a

Sol(vii) 3.14r²

3.14 is the coefficient of r²

Sol(viii) 2(l+b)=2l+2b

2 is the coefficient of l

2 is also the coefficient of b

Sol(ix) 0.1y+0.01y²

0.1 is the coefficient of y

0.01 is the coefficient of y²

Q.4

(a) Identify the term which contains x and give the coefficient of x

(i) y²x+y

(ii) 13y²-8yx

(iii) x+y+2

(iv) 5+z+zx

(v) 1+x+xy

(vi) 12xy²+25

(vii) 7x+xy²

Sol.

Algebraic expression                               terms                                  coefficients

(i) y²x+y                                                      y²x                                         y²

(ii) 13y²-8yx                                              -8yx                                      -8y

(iii) x+y+2                                                   x                                             1

(iv) 5+z+zx                                                 zx                                           z

(v)1+x+xy                                                  xy                                            y

(vi) 12xy²+25                                           12xy²                                    12y²

(vii) 7x+xy²                                              xy²                                        y²

(b) Identify the term which contain y² and give the coefficient of y ²

(i) 8-xy²

(ii) 5y²+7x

(iii) 2x²y-15xy²+7y²

Sol.

Algebraic expression                                       terms                         coefficients

(i) 8-xy²                                                            -xy²                                   -x

(ii) 5y²+7x                                                        5y²                                     5

(iii) 2x²y-15xy²+7y²                                      2x²y                                  2x²

-15xy²                               -15x

7y²                                     7

Q.5

Classify into monomial,binommial and trinomial

(i) 4y-7x

(ii) y²

(iii) x+y-xy

(iv) 100

(v) ab-a-b

(vi) 5-3t

(vii) 4p²q-4pq²

(viii) 7mn

(ix) z²-3z+8

(x) a²+b²

(xi) z²+z

(xii) 1+x+x²

Sol(i) 4y-7x

Binomial

(ii) y²

monomial

(iii) x+y-xy

trinomial

(iv) 100

monomial

(v) ab-a-b

trinomial

(vi) 5-3t

binomial

(vii) 4p²q-4pq²

Binomial

(viii) 7mn

Monomial

(ix) z²-3z+8

Trinomial

(x) a²+b²

Binomial

(xi) z²+z

Binomial

(xii) 1+x+x²

Trinomial

Q.6 State wheather a given pair of term is of like or unlike term

(i) 1,100

(ii) -7x,\frac{5}{2}x

(iii) -29x,-29y

(iv) 14xy,42yx

(v) 4m²p,4mp²

(vi) 12xz,12x²y²

Sol. (i) 1,100

Like term

(ii) -7x,\frac{5}{2}x

Like term because of both variable is the same

(iii) -29x,-29y

Unlike terms because both have different variables

(iv) 14xy,42yx

Like term

(v) 4m²p,4mp²

Unlike terms because the power of m and p is different

(vi) 12xz,12x²y²

Unlike terms because power is different

Q.7 Identify like terms in the following

(a) -xy²,-4yx²,8x²,2xy²,7y,-11x²,-100x,-11yx,20x²y,-6x²,y,2xy,3x

(b)10pq,7p,8q,-p²q²,-7pq,-100q,-23,12q²p²,-5p²,41,2405p,78qp,13p²q,qp²,701p²

Sol.(i)

-xy²    ,  2xy²

4yx²    ,  20x²y

8x²       ,  -11x²

7y         ,    y

-100x    , 3x

-11yx     , 2xy

Sol(ii)

10pq     , -7pq

7p          , 2405p

8q         , -100q

-p²q²   ,  12q²p²

-23       ,  41

-5p²     , 701p²

13p²q   ,  qp²

Algebraic expressions for class 7 exercise 12.2

Q.1 Simply combine like terms

(i) 21b -32 + 7b- 206

(ii) -z2 + 13z2 -5z + 7z3 – 152

(iii) p –(p – q)–q –(q – p)

(iv) 3a–2b-ab–(a–b+ab)+3ab+6–a

(v) 5x2y–5x2+3yx²–3y2+x2–y2+8xy²-3y2

(vi) (3y2+5y–4)–(8y–y2–4)

Sol.

(i) 21b -32 + 7b- 206

21b+7b-32-206

28b-238

(ii) -z2 + 13z² -5z +7z³ – 15z

-z2 +13z²-5z + 7z³ –15z

12z²-5z+7z³ –15z

7z³+12z²-20z

(iii) p –(p – q)–q –(q – p)

p-p+q-q-q+p

p-q

(iv) 3a–2b-ab–(a–b+ab)+3ab+6–a

3a–2b-ab–a+b-ab+3ab+6-a

(v) 5x2y–5x2+3yx²–3y2+x2–y2+8xy²-3y2

5x2y+3yx²-5x²+x²-3y²-y²-3y²+8xy²

8x²y-4x²-7y²+8xy²

(vi) (3y2+5y–4)–(8y–y2–4)

3y²+5y-4-8y+y²+4

4y²-3y

Q.2 Add the following

(i) 3mn,-5mn,8mn,-4mn

(ii) t-8tz,3tz,-z,z-t

(iii) -7mn+5,12mn+2,9mn-8,-2mn-8

(iv) a+b-3,b-a+3,a-b+3

(v) 14x+10y-12xy+13,18-7x-10y+8xy,4xy

(vi) 5m-7n,3n-4m+2,2m-3mn-5

(vii) 4x²y,-3xy²,-5xy²,5x²y

(viii) 3p²q²-4pq+5,-10p²q²,15+9pq+7p²q²

(ix) ab-4a,4b-ab,4a-4b

(x) x²-y²-1,y²-1-x²,1-x²-y²

Sol.

(i) 3mn,-5mn,8mn,-4mn

3mn+(-5mn)+8mn+(-4mn)

3mn-5mn+8mn-4mn

11mn-9mn

2mn

(ii) t-8tz,3tz,-z,z-t

t-8tz+3tz+(-z)+(z-t)

t-5tz-z+z-t

-5tz

(iii) -7mn+5,12mn+2,9mn-8,-2mn-8

-7mn+5+12mn+2+9mn-8+(-2mn-8)

-7mn+5+12mn+2+9mn-8-2mn-8

-7mn+12mn+9mn-2mn+5+2-8-8

-9mn+21mn+7-16

12mn-9

(iv) a+b-3,b-a+3,a-b+3

a+b-3+b-a+3+a-b+3

a-a+a+b+b-b-3+3+3

a+b+3

(v) 14x+10y-12xy+13,18-7x-10y+8xy,4xy

14x+10y-12xy+13+18-7x-10y+8xy+4xy

14x-7x+10y-10y-12xy+8xy+4xy+13+18

7x-315

(vi) 5m-7n,3n-4m+2,2m-3mn-5

5m-7n+3n-4m+2+2m-3mn-5

5m-4m+2m-7n+3n-3mn-5

3m-4n-3mn-5

(vii) 4x²y,-3xy²,-5xy²,5x²y

4x²y+(3xy²)-(5xy²)+5x²y

4x²y+5x²y+3xy²-5xy²

9x²y-2xy²

(viii) 3p²q²-4pq+5,-10p²q²,15+9pq+7p²q²

3p²q²-4pq+5+(-10p²q²)+15+9pq+7p²q²

3p²q²-4pq+5-10p²q²+15+9pq+7p²q²

3p²q²-10p²q²+7p²q²-4pq+9pq+5+15

5pq+20

(ix) ab-4a,4b-ab,4a-4b

ab-4a+4b-ab+4a-4b

0

(x) x²-y²-1,y²-1-x²,1-x²-y²

x²-y²-1+y²-1-x²+1-x²-y²

x²-x²-x²-y²+y²-y²-1-1+1

-x²-y²-1

Q.3 Subtract tthe following

(i) -5y² from y²

(ii) 6xy from -12xy

(iii) (a-b) from (a+b)

(iv) a(b-5) from b(5-a)

(v) -m²+5mn from 4m²-3mn+8

(vi) -x²+10x-5 from 5x-10

(vii) 5a²-7ab+5b² from 3ab-2a²-2b²

(viii) 4pq-5q²-3p² from 5p²+3q²-pq

Sol:

(i) -5y² from y²

y²-(-5y²)

y²+5y²

6y²

(ii) 6xy from -12xy

-12xy-(6xy)

-12xy-6xy

-18xy

(iii) (a-b) from (a+b)

(a+b)-(a-b)

a+b-a+b

0

(iv) a(b-5) from b(5-a)

b(5-a)-{a(b-5)}

5b-ab-ab+5a

5a+5b-2ab

(v) -m²+5mn from 4m²-3mn+8

( 4m²-3mn+8)-(-m²+5mn)

4m²-3mn+8+m²-5mn

5m²-8mn+8

(vi) -x²+10x-5 from 5x-10

5x-10-(-x²+10x-5)

5x-10+x²-10x+5

x²-5x-5

(vii) 5a²-7ab+5b² from 3ab-2a²-2b²

(3ab-2a²-2b²)-(5a²-7ab+5b²)

3ab-2a²-2b²-5a²+7ab+5b²

3ab+7ab-2a²-5a²-2b²+5b²

10ab-7a²+3b²

(viii) 4pq-5q²-3p² from 5p²+3q²-pq

( 5p²+3q²-pq)-(4pq-5q²-3p²)

5p²+3q²-pq-4pq+5q²+3p²

5p²+3p²+3q²+5q²-pq-4pq

8p²+8q²-5pq

Q.4

(a) What should be added to x²+xy+y² to obtain 2x²+3xy?

(b) What should be subtracted from 2a+8b+10 to get -3a+7b+16?

Sol.(a) Let A should be added to x²+xy+y² to obtain 2x²+3xy

x²+xy+y²+A=2x²+3xy

A=2x²+3xy-(x²+xy+y²)

A= 2x²+3xy-x²-xy-y²

A= x²+2xy-y²

Sol(b) Let x should be subtracted from 2a+8b+10 to get -3a+7b+16

(2a+8b+10)-x=-3a+7b+16

2a+8b+10+3a-7b-16=x

x=5a+b-6

Q.5

What should be taken away from 3x²-4y²+5xy+20 to obtain -x²-y²+6xy+20?

Sol: Let A should be subtracted from 3x²-4y²+5xy+20  to obtain -x²-y²+6xy+20

(3x²-4y²+5xy+20)-A=-x²-y²+6xy+20

3x²-4y²+5xy+20+x²+y²-6xy-20=A

A=4x²-3y²-xy

Q.6

(i) From the sum of 3x-y+11 and -y-11 ,subtract 3x-y-11.

(ii) From the sum of 4+3x  and 5-4x+2x², subtract the sum of 3x²-5x and -x²+2x+5.

Sol.(i)

Sum of 3x-y+11 and -y-11 =3x-y+11 +(-y-11)

Sum of 3x-y+11 and -y-11 =3x-y+11 -y-11

=3x-2y

A/Q  , subtract 3x-y-11 from 3x-2y

= (3x-2y)-(3x-y-11)

=3x-2y-3x+y+11

= 11-y

(ii) From the sum of 4+3x  and 5-4x+2x² ,subtract the sum of 3x²-5x and -x²+2x+5.

Sol(ii)

Sum of 4+3x+ 5-4x+2x²=2x²-x+9

Sum of 4+3x+ 5-4x+2x²=2x²-x+9

Another sum

(3x²-5x) +( -x²+2x+5)=3x²-5x-x²+2x+5=2x²-3x+5

A/Q We have to subtract 2x²-3x+5 from 2x²-x+9

=(2x²-x+9)-(2x²-3x+5 )

= 2x²-x+9-2x²+3x-5

= 2x+4

 Algebraic expressions for class 7 exercise 12.3

Q.1 If m=2 ,find the value of

(i) m-2

(ii) 3m-5

(iii) 9-5m

(iv) 3m²-2m-7

(v) \frac{5m}{2}-4

Solution:

(i) m-2

Subtitute m=2

m-2=2-2=0

(ii) 3m-5

Subtitute m=2

3m-5=3(2)-5=6-5=1

(iii) 9-5m

Subtitute m=2

9-5m=9-5(2)=9-10=-1

(iv) 3m²-2m-7

Subtitute m=2

3m²-2m-7=3(2)²-2(2)-7=3(4)-4-7=12-11=1

(v) \frac{5m}{2}-4

Subtitute m=2

\frac{5m}{2}-4=\frac{5(2)}{2}-4=\frac{10}{2}-4=1

Q.2 If p=-2 ,find the value of

(i) 4p+7

(ii) -3p²+4p+7

(iii) -2p³-3p²+4p+7

Solution:

(i) 4p+7

Subtitute p=-2

4p+7=4(-2)+7=-8+7=-1

(ii) -3p²+4p+7

Subtitute p=-2

-3p²+4p+7=-3(-2)²+4(2)+7=-3(4)+8+7=-12+15=3

(iii) -2p³-3p²+4p+7

Subtitute p=-2

-2(-2)³-3(-2)²+4(-2)+7

-2(-8)-3(4)-8+7

+16-12-8+7

4-1

3

Q.3 If a=2 and b=-2 ,find the value of

(i) a²+b²

(ii) a²+ab+b²

(iii) a²-b²

Solution:

(i) a²+b²

Subtitute a=2 and b=-2

a²+b²=(2)²+(-2)²=4+4=8

(ii) a²+ab+b²

Subtitute a=2 and b=-2

(2)²+2(-2)+(-2)²

4-4+4

4

(iii) a²-b²

Subtitute a=2 and b=-2

a²-b²=(2)²-(-2)²=4-4=0

Q.4 When a=0 and b  = -1 ,find the value of the given expressions

(i) 2a+2b

(ii) 2a²+2b²+1

(iii) 2a²b+2ab²+ab

(iv) a²+ab+2

Solution:

(i) 2a+2b

Subtitute a=0 and b = -1

2a+2b

2(0)+2(-1)

0-2

-2

(ii) 2a²+2b²+1

Subtitute a=0 and b = -1

2(0) +2(-1)²+1

0+2+1

3

(iii) 2a²b+2ab²+ab

Subtitute a=0 and b = -1

2(0)²(-1)+2(0)(-1)²+0(-1)

0+0+0

0

(iv) a²+ab+2

Subtitute a=0 and b = -1

(0)²+0(-1)+2

0+0+2

2

Q.5 Simply the expressions and find the value if x equal to 2

(i) x+7+4(x-5)

(ii) 3(x+2) +5x-7

(iii) 6x+5(x-2)

(iv) 4(2x-1) +3x+11

Solution:

(i) x+7+4(x-5)

x+7+4x-20

5x-13

Subtitute x=2

5(2)-13

10-13

-3

(ii) 3(x+2) +5x-7

3x+6+5x-7

8x-1

Subtitute x=2

8(2)-1

16-1

15

(iii) 6x+5(x-2)

6x+5x-10

11x-10

Subtitute x=2

11(2)-10

22-10

12

(iv) 4(2x-1) +3x+11

8x-4+3x+11

11x-7

Subtitute x=2

11(2)-7

22-7

15

Q.6 Simplify these expressions and find the value if x=3,a=-1,b=-2.

(i) 3x-5-x+9

(ii) 2-8x+4x+4

(iii) 3a+5-8a+1

(iv) 10-3b-4-55

(v) 2a-2b-4-5+a

Solution:

(i) 3x-5-x+9

2x+4

Subtitute x=3

2(3)+4

6+4

10

(ii) 2-8x+4x+4

6-4x

Subtitute x=3

6-4(3)

6-12

-6

(iii) 3a+5-8a+1

-5a+6

Substitute a=-1

-5(-1)+6

5+6

11

(iv) 10-3b-4-55

10-3b-59

-3b-49

Substitute b=-2

-3(-2)-49

6-49

-43

Q.7

(i) If z=10 ,find the value of z²-3(z-10)

(ii) If p=-10 ,find the value of p²-2p-100

Solution:

(i) First of all ,simply the expression

z²-3(z-10)

z²-3z+30

Now , substitute z=10

(10)²-3(10) +30

100-30+30

100

(ii) p²-2p-100

Put p=-10

p²-2p-100

(-10)²-2(-10)-100

100+20-100

20

Q.8 What should be the value of a if the value of  2x2 + x – a equals to 5,x=0?

Solution: It is given that

2x2 + x – a=5

Subtitute x=0 in above equation

2(0)²+0-a=5

0+0-a=5

a=-5

Q.9 Simplify the expression and find its value when a=5 and b=-3

2(a²+ab)+3-ab

Solution:

2a²+2ab+3-ab

2a²+ab+3

Subtitute a=5 and b=-3

2(5)²+(5)(-3)+3

2(25)-15+3

50-12

38

 

 

 

 

 

 

 

 

 

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