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Question

Simplify the following:

(i) (1.5x4y)(1.5x+4y+3)

(ii) (x+y)(2x+y)+(x+2y)(xy)

(iii) (a2+5)(b3+3)+5

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Solution

(i) (1.5x4y)(1.5x+4y+3)


=(1.5x×1.5x)+(1.5x×4y)+(1.5x×3)(4y×1.5x)(4y×4y)(4y×3)

=2.25x2+6xy+4.5x6xy16y212y

=2.25x216y2+4.5x12y


(ii) (x+y)(2x+y)+(x+2y)(xy)


=(x×2x)+(x×y)+(y×2x)+(y×y)+(x×x)(x×y)+(2y×x)(2y×y)

=2x2+xy+2xy+y2+x2+xy2y2

=3x2+4xyy2


(iii) (a2+5)(b3+3)+5


=(a2×b3+a2×3+5×b3+5×3)+5

=a2b3+3a2+5b3+15+5

=a2b3+3a2+5b3+20


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