25(a+b)^2-9(a-b)^2

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25(a+b)^2-9(a-b)^2
25(a+b)^2-9(a-b)^2

25(a+b)^2-9(a-b)^2
[5(a+b)+3(a-b)][5(a+b)-3(a-b)]
=4(4a+b)((a+4b)


25(a+b)²-9(a-b)²
=[5(a+b)]²-[3(a-b)]²
=[5(a+b)+3(a-b)][5(a+b)-3(a-b)]
=(8a+2b)(2a+8b)
=4(4a+b)(a+4b)

5^2(a+b)^2-3^2(a-b)^2
=(5a+5b)^2-(3a-3b)^2
=(5a+5b+3a-3b)(5a+5b-3a+3b)
=(8a+2b)(2a+8b)

原式==[5(a+b)]2-[3(a-b)]2
=[5(a+b)+3(a-b)][5(a+b)-3(a-b)]
=(8a+2b)(2a+8b)
=2(4a+b)(a+4b)