Question

factorize
9{a+b}² -12{a²-b²} +4{a²-b²}

Answer 1

Step-by-step explanation:

9(a^2+2ab+b^2)-12(a^2-2ab+b^2)+4(a^2-2ab+b^2)

9a^2+18ab+9b^2-12a^2+24ab-12b^2+4a^2-8ab

+4b^2

a^2+34ab+b^2

a^2+17ab+17ab+b^2

17a(a+b) +17b(a+b)

(a+b) (17a+17b) =0

17(a+b) (a+b) =0

17(a^2+b^2) =0

Therefore a^2+b^2=0

Answer 2

/* There is a mistake in last term . It may be like this*/

$9(a+b)^{2} - 12(a^{2} - b^{2}) + 4(a- b)^{2}$

$= [3(a+b)^{2} - 2 \times [3(a+b)]\times [2(a-b)] + [2(a-b)]^{2}$

$= [ 3(a+b) - 2(a-b)]^{2} \\= (3a+3b-2a+2b)^{2} \\= (a+5b)^{2} \\= (a+5b)(a+5b)$

Therefore.

$\red{Factors\: 9(a+b)^{2} - 12(a^{2} - b^{2}) + 4(a- b)^{2}}$

$\green {= (a+5b)(a+5b) }$

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