Question

七年级因式分解题，要过程。

1.x²(y²-9)+4(9-y²)
2.(x-2y)²-3(x-2y)-10
3.6(x^n+1)+5(x^n)y-4(x^n-1)y²
4.9-a²-b²+2ab
5.x²-2xy+y²+4x-4y+4
6.(x+y)²-4(x+y+-1)
7.(ax+by)²+(bx-ay)²
8.(c-a)²-4(b-c)(a-b)

Answer 1

1.x2(y2-9)+4(9-y2)=(y2-9)(x2-4)=(y+3)(y-3)（x+2）(x-2)
2.(x-2y)2-3(x-2y)-10=(x-2y-5)(x-2y+2)
3.6(x^n+1)+5(x^n)y-4(x^n-1)y2=(x^n-1)(6x^2+5xy-4y^2)
=(x^n-1)*(2x-y)(3x+4y)
4.9-a2-b2+2ab=9-(a-b)2=(3-a+b)(3+a-b)
5.x2-2xy+y2+4x-4y+4=(x-y)2+4(x-y)+4=(x-y+2)2
6.(x+y)2-4(x+y+-1)=(x+y)2-4(x+y)+4=(x+y-2)2
7.(ax+by)2+(bx-ay)2=(ax)2+(by)2+2abxy+(bx)2+
(ay)2-2abxy=(a2+b2)x2+(a2+b2)y2=(a2+b2)(x2+y2)
8.(c-a)2-4(b-c)(a-b) =(c)2-2ca+(a)2-4ab+4(b)2+4ac-4bc=(c)2+2ca+(a)2-+4ab+4(b)2-4bc=(a+c-2b)2

Answer 2

1.x²(y²-9)+4(9-y²)=（x+2）(x-2)(y+3)(y-3)
2.(x-2y)²-3(x-2y)-10=(x-2y-5)(x-2y+2)
3.6(x^n+1)+5(x^n)y-4(x^n-1)y²=(x^n-1)*(2x-y)(3x+4y)
4.9-a²-b²+2ab=3-(a-b)²=(3-a+b)(3+a-b)
5.x²-2xy+y²+4x-4y+4=(x-y+2)²
6.(x+y)²-4(x+y+-1)=(x+y-2)²
7.(ax+by)²+(bx-ay)²=(a²+b²)(x²+y²)
8.(c-a)²-4(b-c)(a-b) =(a+c+2b)²