Question

十字相乘法分解因式的习题

Answer 1

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)