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Question

Expand using a formula.

(1) (2a + 3b + 3)2
(2) (x + 10) (x − 11)
(3) 3x+13x3
(4) (2m − n)3
(5) (2x + 3) (2x − 7)

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Solution

(1) We know that a+b+c2=a2+b2+c2+2ab+2bc+2ca
Thus, 2a+3b+32=4a2+9b2+9+12ab+18b+12a

(2) (x + 10) (x − 11)
We know that (x+a)(x+b) = x2+(a+b)x+ab
=x2+(10-11)x+10×(-11)=x2-x-110 x+10 x-11=x2-x-110

(3) We know that a+b3=a3+b3+3a2b+3ab2
Thus, 3x+13x3=27x3+127x3+9x+1x

(4) We know that a+b3=a3+b3+3a2b+3ab2
2m-n3=8m3-n3-12m2n+6mn2

(5) (2x + 3) (2x − 7)
We know that (x+a)(x+b) = x2+(a+b)x+ab
=4x2-14-6+3×(-7)=4x2-8x-21 2x+3 2x-7=4x2-8x-21

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