分解因式:9(2a+5b)^2-(3a-4b)^2

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分解因式:9(2a+5b)^2-(3a-4b)^2
分解因式:9(2a+5b)^2-(3a-4b)^2

分解因式:9(2a+5b)^2-(3a-4b)^2
9(2a+5b)^2-(3a-4b)^2
=[3(2a+5b)+(3a-4b)][3(2a+5b)+(3a-4b)]
=(6a+15b+3a-4b)(6a+15b-3a+4b)
=(9a+11b)(3a+19b)

9(2a+5b)^2-(3a-4b)^2=3^2(2a+5b)^2-(3a-4b)^ =[3(2a+5b)+(3a-4b)]-[3(2a+5b)-(3a-4b)] =(9a+11b)-(3a+19b) =6a-8b

27a^2+204ab+169b^2

9(2a+5b)^2-(3a-4b)^2 =[3(2a+5b)+(3a-4b)][3(2a+5b)+(3a-4b)] =(6a+15b+3a-4b)(6a+15b-3a+4b) =(9a+11b)(3a+19b) =27a^2+204ab+169b^2