Question

因式分解1.(a²+b²)²-4a²b² 2.x²-y²-x-y

Answer 1

1.(a²+b²)²-4a²b²
原式=(a²+b²)²-(2ab)²
=(a²+b²+2ab)(a²+b²-2ab)
=(a+b)²(a-b)²
2.x²-y²-x-y
原式=(x²-y²)-(x+y)
=(x+y)(x-y)-(x+y)
=(x+y)(x-y-1)

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Answer 2

.(a²+b²)²-4a²b²=a^4+b^4+2a^2b^2-4a^2b^2=a^4+b^4-2a^2b^2=(a^2-b^2)2=(a+b)^2(a-b)^2

x²-y²-x-y=(x^2-y^2)-(x+y)=(x+y)(x-y)-(x+y)=(x+y)(x-y-1)

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