Worksheet on multiplication of binomial with a monomial

Q.1 Multiply

(i) -9xy by -2x²y+3x 

(ii) 2x³y by (-3xy+xy²) 

Q.2 Multiply -3x²y by 7x³y -5xy² .Find the value of the product by taking x=- 2 and  y=-1 

Q.3 Find the product of the following and find the value of the product by taking x= -3 and y=2 

(i) 3x and y+13x 

(ii) 5xy and (x+y) 

Q.4 Simplify 

2xy(x-4)+5y and find its value for (i) x=2 ,y=-1 

Q.5 Add :

(i) x(x+y) ;y(y+z);z(z+x)

(ii) 3m(1-m-n) and 2n(m-n-1) 

Q.6 Subtract 

(i) 2x(x-3y+4z) from x(7x-y+9z) 

(ii) (a-b+c) – 2(-a+b-c) from 5(a+2b-c) 

Solution: 

Problem: 01

Multiply

(i) -9xy by -2x²y+3x 

(ii) 2x³y by (-3xy+xy²) 

Solution (i) : 

(-9xy)×( -2x²y+3x )= -9xy ×(-2x²y)+(-9xy)×(3x) 

(-9xy)×( -2x²y+3x )={-9×-2}{xy×x²y}+{-9×3}{xy×x}

(-9xy)×( -2x²y+3x )=18{x³y²}+{-27}{x²y}

(-9xy)×( -2x²y+3x )=18x³y²-27x²y

Solution(ii) : 

2x³y by (-3xy+xy²) 

(2x³y)× (-3xy+xy²) =2x³y×(-3xy)+2x³y×xy²

(2x³y)× (-3xy+xy²) ={2×-3}{x³y×xy}+{2}{x³y×xy²}

(2x³y)× (-3xy+xy²) =-6 x^4y²+2x^4

(2x³y)× (-3xy+xy²) =-6 x^4y² + 2x^4

Problem: 02 Multiply -3x²y by 7x³y -5xy² .Find the value of the product by taking x=- 2 and  y=-1 

Solution: 

(-3x²y)×(7x³y -5xy²)=(-3x²y)×(7x³y)-(-3x²y)×(5xy²)

(-3x²y)×(7x³y -5xy²)={-3×7}{x²y×x³y}-{-3×5}{x²y×xy²}

(-3x²y)×(7x³y -5xy²)=-21x^5y²-{-15}{x³y³}

(-3x²y)×(7x³y -5xy²)=-21x^5y²+15x³y³

substitute x=-2 and y=-1 

=-21x^5y²+15x³y³

= -21(-2)^5(-1)²+15(-2)³(-1)³

= -21 (-32)(1)+15(-8)(-1)

= 672+120 

= 792 

Problem: 03  Find the product of the following and find the value of the product by taking x= -3 and y=2 

(i) 3x and y+13x 

(ii) 5xy and (x+y) 

Solution: (i) 

(3x)×(y+13x)=(3x)×(y)+(3x)×(13x) 

(3x)×(y+13x)=3xy + 39x²

Substitute x=-3 and y=2 

=3xy + 39x²

=3(-3)(2)+39(-3)²

=-18+39(9)

=333

Solution:(ii) 

5xy and (x+y) 

(5xy)×(x+y)=(5xy)(x)+5xy(y)

(5xy)×(x+y)=5x²y+5xy²

Substitute x=-3 and y=2 

=5x²y+5xy²

=5(-3)²(2)+5(-3)(2)

=5(9)(2)-30 

=90-30

=60 

Problem : 04 Simplify 

2xy(x-4)+5y and find its value for (i) x=2 ,y=-1 

Solution: 

2xy(x-4)+5y

= 2x²y-8xy+5y

Substitute x=2 and y=-1 

= 2x²y-8xy+5y

= 2(2)²(1)-8(2)(-1)+5(-1) 

= 2(4)+16-5

=8+11 

=19 

Problem : 05 Add :

(i) x(x+y) ;y(y+z);z(z+x)

(ii) 3m(l-m-n) and 2n(m-n-l) 

Solution: (i) 

x(x+y) ;y(y+z);z(z+x)

x(x+y)+y(y+z)+z(z+x)

=x²+xy+y²+yz+z²+zx

=x²+y²+z²+xy+yz+zx

Solution : (ii) 

3m(l-m-n) and 2n(m-n-l) 

3ml-3m²-3mn and 2mn-2n²-2nl,

3ml-3m²-3mn + 2mn-2n²-2n

3ml-3m²-mn-2n²-2nl 

Problem: 06  Subtract 

(i) 2x(x-3y+4z) from x(7x-y+9z) 

(ii) (a-b+c) – 2(-a+b-c) from 5(a+2b-c) 

Solution:(i) 

2x(x-3y+4z) from x(7x-y+9z)

2x²-6xy+8xz from 7x²-xy+9xz 

(7x²-xy+9xz )-(2x²-6xy+8xz) 

7x²-xy+9xz -2x²+6xy-8xz 

5x²+5xy+xz 

Solution (ii) 

(a-b+c) – 2(-a+b-c) from 5(a+2b-c)

(a-b+c)+2a-2b+2c from 5(a+2b-c) 

a-3b+3c from 5a+1ob-5c 

(5a+1ob-5c )-(a-3b+3c) 

5a+10b-5c-a+3b-3c 

4a +13b-8c 

Check these resources as well 

Leave a Comment