因式分解 (a+b)²-1 -(x+2)²+16(x-1)² (3x+2y)²-(x-y)²

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因式分解(a+b)²-1-(x+2)²+16(x-1)²(3x+2y)²-(x-y)²因式分解(a+b)²-1-(x+2)²+16

因式分解 (a+b)²-1 -(x+2)²+16(x-1)² (3x+2y)²-(x-y)²
因式分解 (a+b)²-1 -(x+2)²+16(x-1)² (3x+2y)²-(x-y)²

因式分解 (a+b)²-1 -(x+2)²+16(x-1)² (3x+2y)²-(x-y)²
(a+b)²-1
=(a+b+1)(a+b-1)
-(x+2)²+16(x-1)²
=[4(x-1)+(x+2)][4(x-1)-(x+2)]
=(4x-4+x+2)(4x-4-x-2)
=(5x-2)(3x-6)
=3(x-2)(5x-2)
(3x+2y)²-(x-y)²
=[(3x+2y)+(x-y)][(3x+2y)-(x-y)]
=(3x+2y+x-y)(3x+2y-x+y)
=(4x+y)(2x+3y)

(a+b)²-1
=(a+b+1)(a+b-1)

-(x+2)²+16(x-1)²
=(4(x-1))^2-(x+2)^2
=(4(x-1)-(x+2))(4(x-1)+(x+2)
=(4x-4-x-2)(4x-4+x+2)
=(3x-6)(5x-2)
=3(x-2)(5x-2)

...

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(a+b)²-1
=(a+b+1)(a+b-1)

-(x+2)²+16(x-1)²
=(4(x-1))^2-(x+2)^2
=(4(x-1)-(x+2))(4(x-1)+(x+2)
=(4x-4-x-2)(4x-4+x+2)
=(3x-6)(5x-2)
=3(x-2)(5x-2)

(3x+2y)²-(x-y)²
=(3x+2y-(x-y))(3x+2y+(x-y))
=(3x+2y-x+y)(3x+2y+x-y)
=(2x+3y)(4x+y)

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