因式分解1.(x^2-y^2)(x+y)-(x-y)^3 2.（a-b）^4-(b-a)^2 3.x^4-x^2 急

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因式分解1.(x^2-y^2)(x+y)-(x-y)^3 2.（a-b）^4-(b-a)^2 3.x^4-x^2 急
因式分解1.(x^2-y^2)(x+y)-(x-y)^3 2.（a-b）^4-(b-a)^2 3.x^4-x^2 急

因式分解1.(x^2-y^2)(x+y)-(x-y)^3 2.（a-b）^4-(b-a)^2 3.x^4-x^2 急
(x²-y²)(x+y)-(x-y)³
=(x-y)(x+y)²-(x-y)³ 提取公因式(x-y)
=(x-y)[(x+y)²-(x-y)²] 中括号内运用平方差公式分解
=(x-y)[(x+y)+(x-y)][(x+y)-(x-y)]
=(x-y)×2x▪2y
=4xy(x-y)
(a-b)^4-(b-a)²
=(a-b)^4-[-1×(a-b)]²
=(a-b)^4-(-1)²×(a-b)²
=(a-b)^4-(a-b)² 提取公因式(a-b)²
=(a-b)²[(a-b)²-1] 中括号内运用平方差公式分解
=(a-b)²[(a-b)+1][(a-b)-1]
=(a-b)²(a-b+1)(a-b-1)
x^4-x² 提取公因式x²
=x²(x²-1)
=x²(x+1)(x-1)

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