因式分解(公式法)4(x+2y)^2-9(x-y)^2x^(n+3)-x^(n-1)

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因式分解(公式法)4(x+2y)^2-9(x-y)^2x^(n+3)-x^(n-1)因式分解(公式法)4(x+2y)^2-9(x-y)^2x^(n+3)-x^(n-1)因式分解(公式法)4(x+2y)

因式分解(公式法)4(x+2y)^2-9(x-y)^2x^(n+3)-x^(n-1)
因式分解(公式法)
4(x+2y)^2-9(x-y)^2
x^(n+3)-x^(n-1)

因式分解(公式法)4(x+2y)^2-9(x-y)^2x^(n+3)-x^(n-1)
4(x+2y)^2-9(x-y)^2=[2(x+2y)+3(x-y)][2(x+2y)-3(x-y)] (平方差公式)
=-(5x+y)(x-7y)
x^(n+3)-x^(n-1)=x^(n-1)(x^4-1) (提取公因式的最低次方)
=x^(n-1)(x^2+1)(x^2-1) (平方差公式)
=x^(n-1)(x^2+1)(x-1)(x +1) (平方差公式)

4(x+2y)^2-9(x-y)^2=[2(X+2Y)]^2-[3(X-Y)]^2=[2(X+2Y)+3(X-Y)]*[2(X+2Y)-3(X-Y)]=(5X-Y)(-X+7Y)
x^(n+3)-x^(n-1)=X^n*(X^3-1/X)

4(x+2y)^2-9(x-y)^2=(2x+4y)^2-(3x-3y)^2=(2x+4y+3x-3y)(2x+4y-3x+3y)=(5x+y)(7y-x)=-5x^2+34xy+7y^2.
x^(n+3)-x^(n-1)=x^(n-1)(x^2+1)(x-1)(x +1)