Question

因式分解(x+y)²-(x-y)²

分解因式8（x²-2y²）-x（7x+y）+xy

Answer 1

(x+y)²-(x-y)²
=[(x+y)-(x-y)][(x+y)+(x-y)]
=(2y)(2x)
=4xy

8(x²-2y²)-x(7x+y)+xy
=8x²-16y²-7x²-xy+xy
=x²-16y²
=(x+4y)(x-4y)

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Answer 2

(x+y)²-(x-y)²
=[(x+y)+(x-y)][(x+y)-(x-y)]
=2x×2y
=4xy

8（x²-2y²）-x（7x+y）+xy
=8x²-16y²-7x²-xy+xy
=x²-16y²
=(x+4y)(x-4y)

Answer 3

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

8（x²-2y²）-x（7x+y）+xy
=8x²-16y²-7x²-xy+xy
=x²-16y²
=(x+4y)(x-4y)

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Answer 4

8（x²-2y²）-x（7x+y）+xy=8x²-16y²-7x²-yx+xy=x²-16y²=(x-4y)(x+4y)