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

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