十字相乘法分解因式的习题
1个回答

1.2*（x+y）^2+(x+y)(c+d)-6（c+d）^2

2.21a^2-13ab+2b^2

3.(x-y)^2-3(x-y)-10

4.x^(n+1)-3x^n+2x^(n+2)

答案

1.2*（x+y）^2+(x+y)(c+d)-6（c+d）^2

令k=x+y ,h=c+d

原式=2k^2+kh-6h^2

=(2k-3h)(k+2h)

=(2x+2y-3c-3d)(x+y+2c+2d)

.

2.21a^2-13ab+2b^2

=(3a-b)(7a-2b)

.

3.(x-y)^2-3(x-y)-10

令k=x-y

原式=k^2-3k-10

=(k-5)(k+2)

=(x-y-5)(x-y+2)

.

4.x^(n+1)-3x^n+2x^(n+2)

=(x^n)(x)-3x^n+(x^n)(2x^2)

=(x^n)(2x^n+x-3)

=(x^n)(2x+3)(x-1)

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