# Worksheet on Multiplication of binomials

Q.1 Simplify

(i) (a²+b²)(a+b)

(ii) (3x²-y²)(10x²-3y²)

(iii) 3x(-6x+11y)-(5x+12y)(2x+9y)

(iv) 7x(2x-3)-9x(2x²)-5x(2x+3)

Q.2 Simplify this

(7x-9y²)(2x²-3y)-(5x+2y)(9x-10y)-2x(3x+5y)

Q.3 Find the following products

(i) (10a-11b)(5a+1)

(ii) (1 – x3) × (x2 + 2)

Answer

Problem: 01

Simplify

(i) (a²+b²)(a+b)

(ii) (3x²-y²)(10x²-3y²)

(iii) 3x(-6x+11y)-(5x+12y)(2x+9y)

(iv) 7x(2x-3)-9x(2x²)-5x(2x+3)

Solution:(i)

(a²+b²)(a+b) =a²(a+b)+b²(a+b)

(a²+b²)(a+b) =a³+a²b+b²a+b³

(a²+b²)(a+b) =a³+b³+ab(a+b)

Solution :(ii)

(3x²-y²)(10x²-3y²)=3x²(10x²-3y²)-y²(10x²-3y²)

(3x²-y²)(10x²-3y²)=30x^4-9x²y²-10x²y²+3y^4

(3x²-y²)(10x²-3y²)=30x^4+3y^4-19x²y²

Solution:(iii)

3x(-6x+11y)-(5x+12y)(2x+9y) =(-18x²+33xy)-{5x(2x+9y)+12x(2x+9y)}

3x(-6x+11y)-(5x+12y)(2x+9y) =-18x²+33xy-{10x²+45xy+24x²+108xy}

3x(-6x+11y)-(5x+12y)(2x+9y) =-18x²+33xy-10x²-45xy-24x²-108xy

3x(-6x+11y)-(5x+12y)(2x+9y) =-52x² – 75xy

Solution: (iv)

7x(2x-3)-9x(2x²)-5x(2x+3) = 14x²-21x-18x³-10x²-15x

7x(2x-3)-9x(2x²)-5x(2x+3) =-18x³ +4x²-36x

Problem: 02

Simplify this

(7x-9y²)(2x²-3y)-(5x+2y)(9x-10y)-2x(3x+5y)

Solution :(2)

(7x-9y²)(2x²-3y)-(5x+2y)(9x-10y)-2x(3x+5y)

= 7x(2x²-3y)-9y²(2x²-3y)-5x(9x-10y)+2y(9x-10y)-6x²-10xy

= 14x³-21xy-18x²y²+21y³-45x²+50xy+18xy-20y²-6x²-10xy

= 14x³-18x²-51x²+9xy+20y²+27y³

Problem: 03

Find the following products

(i) (10a-11b)(5a+1)

(ii) (1 – x3) × (x2 + 2)

Solution(i)

(10a-11b)(5a+1)

=50a²+10a-55ab-11b

=50a²+10a-55ab-11b

Solution(ii)

(1 – x3) × (x2 + 2)

= x²+2-x^5-2x³

=x^5-2x³+x²+2

check these resources as well

Don’t forget to share your feedback in comment section ;