9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b)分解因式

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9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b)分解因式9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b)分解因式9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b

9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b)分解因式
9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b)分解因式

9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b)分解因式
平方差
原式=[3(2a+3b)]²-[2(3a-2b)]²
=(6a+9b)²-(6a-4b)²
=(6a+9b+6a-4b)(6a+9b-6a+4b)
=13b(12a+5b)

9(2a+3b)(2a+3b)-4(3a-2b)(3a-2b)
=[3(2a+3b)+2(3a-2b)][3(2a+3b)-2(3a-2b)]
=13b*(12a+5b)

原式=9(2a+3b)^2-4(9a^2-4b^2)
=9(4a^2+12ab+9b^2)-36a^2+16b^2
=36a^2+108ab+81b^2-36a^2+16b^2
=97b^2+108ab