Algebraic Expressions for class 7[Full Chapter in one Place]

In previous classes, you’ve read the basics of algebra. Now in class 7, you will read about algebra in more detail. In this article, we’re going to discuss the basics of “Algebra”, “Ncert solution” and practice questions at the end. 

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

Constants: Constants are real numbers or numerical values that are significant(which can’t be changed ).

For Example:  5,15,45…..etc

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

For Example 6+n,n,x….etc, the value of these quantities may vary with the equation.

Algebraic expressions for class 7

Algebraic Expression: 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 are algebraic expression .

Terms of the Algebraic expressions

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

For Example: In 8a-4b+11 ; 8a,-4b, and 11 are its terms

Factors of a term

A term can be the product of variables, constants or variable and constant both. For Example : 

8a is a term that is the product of a constant and a variable whereas Term “11” is the product of only constants(1,11) . We use a “tree Diagram ” to represent terms and factors of an algebraic expression.

Tree diagram 

It is a type of diagram which is used to represent the “Terms” and “factors” of an algebraic expression. It looks something like this 

Tree diagram class 7

✔  Continuous lines are used to represent terms of expression. Whereas,

  Dotted lines are used to represent factors of expression.

For Example : 

Tree diagram example

 

 

Coefficient

Coefficient: Any factor of the term is called the coefficients of the remaining factors. It can 

A Numerical factor

An algebraic factor

A product of two or more factors.

For Example: In 9ab²

⇒ 9 is the Numerical coefficient of other remaining factors ( i.e ab²) 

⇒ a is the coefficient of 9b² whereas

⇒ b² is the factor of 9a  

Constant term 

Numerical terms in an algebraic expression are known as Constant term. For example : 

  •  In the algebraic expressions 12x²+15y²-16, the constant term is -16.
  • And, In 8x²y-6z, as there is no constant term, we consider 0 as the constant term.

Like term

Terms having the same variables and equivalent powers is called Like term. For example

2x²,3x²,-18x²are like terms, And  13ab²,24ab² is an example of another like term.

Unlike terms

Terms don’t have the same variables and equivalent powers are known as, Unlike term.For Example : 

4p,10mn are unlike terms, And 3a,3a² are also examples of an, Unlike term.

Types of Algebraic expression 

Basically, on the basis of ” number of terms”  in the Expression. Algebraic expressions is generally classified into 5 category 

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

For Example 15cd, 100 and a³b²c² are monomials 

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

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

Trinomial: An expression that 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 are Quadrinomial .

Polynomial: An expression containing one or more terms collectively known as Polynomial.It contains Monomials,Binomials ,Trinomials ,Quadrinomial .

Algebraic expressions for class 7 ncert solution

Ncert solution class 7 ex 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 factors 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 

5  

 -4×x

5

(b)-4x+5y  -4x 

5y   

 -4×x

5y 

(c) 5y+3y²  5y   

3y²   

 5×y

3×y×y

(d) xy+2x²y²      xy     

2x²y²

  x×y

2×x×x×y×y

(e) pq+q    5y   

3y²   

5×y

  3×y×y

(f) )1.2ab-2.4b+3.6a  1.2ab     

-2.4b   

3.6a 

1.2×a×b

2.4×b×-1

 3.6×a

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

\frac{1}{4}

\frac{3}{4}×x

\frac{1}{4}

(h) 0.1p²+0.2q² 0.1p² 

0.2q²     

 0.1×p×p

 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
(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

 

(b) Identify the term which contains 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 

-15xy² 

7y² 

2x²

-15x

 7

Q.5

Classify into monomial,binomial 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)

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}xLike 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 term 

(vi) 12xz,12x²y² – Unlike term 

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.(a)

-xy² 4yx² 8x² 7y  -100x    -11yx
2xy² 20x²y -11x²   y 3x 2xy

Sol (b)

10pq  7p  8q -p²q² -23  -5p² 13p²q 
-7pq 2405p -100q 12q²p² 41 701p² 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

Substitute m=2

m-2=2-2=0

(ii) 3m-5

Substitute m=2

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

(iii) 9-5m

Substitute m=2

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

(iv) 3m²-2m-7

Substitute 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

Substitute a=2 and b=-2

a²+b²=(2)²+(-2)²=4+4=8

(ii) a²+ab+b²

Substitute a=2 and b=-2

(2)²+2(-2)+(-2)²

4-4+4

4

(iii) a²-b²

Substitute 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

Substitute a=0 and b = -1

2a+2b

2(0)+2(-1)

0-2

-2

(ii) 2a²+2b²+1

Substitute a=0 and b = -1

2(0) +2(-1)²+1

0+2+1

3

(iii) 2a²b+2ab²+ab

Substitute 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

Substitute x=2

5(2)-13

10-13

-3

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

3x+6+5x-7

8x-1

Substitute x=2

8(2)-1

16-1

15

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

6x+5x-10

11x-10

Substitute x=2

11(2)-10

22-10

12

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

8x-4+3x+11

11x-7

Substitute 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

Substitute x=3

2(3)+4

6+4

10

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

6-4x

Substitute 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

Substitute 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

Substitute a=5 and b=-3

2(5)²+(5)(-3)+3

2(25)-15+3

50-12

38

Frequently Asked Questions 

Q.1 What are Algebraic Expressions give examples? 

Answer: 

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 are algebraic expression .

Q.2 What are expressions Explain? 

Answer: 

Expressions are nothing but statements which contain at least two terms (Either Constant or Variable ) connected with minimum one mathematical operator (+,-,×,÷) 

Example : x+3 ,2x,12+4 etc are example of Expression .

Q.3 How to solve any algebraic Expression? 

Solution: 

21b -32 + 7b- 206

Add Like Terms 

21b + 7b -32 -206

28b-238

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