Question

分解因式：16（a+b)²-9(a-b)²

Answer 1

16(a b)^2-9(a-b)^2
=[4(a b)]^2-[3(a-b)]^2
=(4a 4b)^2-(3a-3b)^2
=[(4a 4b) (3a-3b)][(4a 4b)-(3a-3b)]
=(4a 4b 3a-3b)(4a 4b-3a 3b)
=(7a b)(a 7b)
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Answer 2

16（a+b)²-9(a-b)²
=[4(a+b)+3(a-b)][4(a+b)-3(a-b)]
=(4a+4b+3a-3b)(4a+4b-3a+3b)
=(7a+b)(a+7b)

追问

9(x-3)²-4(2-3x)²
-4(x-y)²＋16z²

追答

9(x-3)²-4(2-3x)²
=[3(x-3)+2(2-3x)][3(x-3)-2(2-3x)]
=(3x-9+4-6x)(3x-9-4+6x)
=(-3x-5)(9x-13)
=-(3x+5)(9x-13)

-4(x-y)²＋16z²
=[4z-2(x-y)][4z+2(x-y)]
=(4z-2x+2y)(4z+2x-2y)
=4(2z-x+y)(2z+x-y)

追问

再麻烦一下，我真心做不来。
169x²-196y²
(2x+y)²-(x+2y)²

追答

169x²-196y²
=(13x+14y)(13x-14y)

(2x+y)²-(x+2y)²
=(2x+y+x+2y)(2x+y-x-2y)
=(3x+3y)(x-y)
=3(x+y)(x-y)

Answer 3

16（a+b)²-9(a-b)²
=[4(a+b)+3(a-b)]x[4(a+b)-3(a-b)]
=(7a+b)x(a+7b)

追问

9(x-3)²-4(2-3x)²
-4(x-y)²＋16z²