# 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

(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

(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