Question

因式分解

（1）4m²-（m+n）²
（2）5a²b（x-y）三次方-30ab²（y-x）²
（3）（x²+y²）²-4x²y²
（4）x²-2xy+y²-9
（5）x（x-1）+(x-1)²
（6）(x²-1)²+6（1-X²）+9

Answer 1

1）4m²-（m+n）²=(2m+m+n)(2m-m-n)=(3m+n)(m-n)
（2）5a²b（x-y）三次方-30ab²（y-x）²
=5a²b（x-y）三次方-30ab²（x-y）²
=5ab(x-y)^2(ax-ay-6b)
（3）（x²+y²）²-4x²y²
=(x^2+y^2+2xy)(x^2+y^2-2xy)
=(x+y)^2(x-y)^2
（4）x²-2xy+y²-9
=(x-y)^2-3^2
=(x-y+3)(x-y-3)
（5）x（x-1）+(x-1)²
=(x-1)(x+x-1)
=(x-1)(2x-1)

（6）(x²-1)²+6（1-X²）+9
=(x²-1)²-6（X²-1）+9
=(x^2-1-3)^2
=(x+2)^2(x-2)^2

Answer 2

1.4m^2-(m n)^2
=(2m m n)(2m-m-n)
=(3m n)(m-n)
2.5a^2b(x-y)^3-30ab^2(y-x)^2
=5a^2b(x-y)^3-30ab^2(x-y)^2
=5ab(x-y)^2[a(x-y)-6b]
=5ab(x-y)^2(ax-ay-6b)
3.(x^2 y^2)^2-4x^2y^2
=(x^2 y^2 2xy)(x^2 y^2-2xy)
=(x y)^2(x-y)^2
4.x^2-2xy y^2-9
=(x-y)^2-9
=(x-y-3)(x-y 3)
5.x(x-1) (x-1)^2
=(x-1)(x x-1)
=(x-1)(2x-1)
6.(x^2-1)^2 6(1-x^2) 9
=(x^2-1)^2-6(X²-1) 9
=(x^2-1-3)^2
=(x 2)^2(x-2)^2

Answer 3

（1）4m²-（m+n）²
=[2m+(m+n)][2m-(m+n)]
=(3m+n)(m-n)
（2）5a²b（x-y）三次方-30ab²（y-x）²
=5ab(x-y)^2[a(x-y)-6b]
=5ab(x-y)^2(ax-ay-6b)
（3）（x²+y²）²-4x²y²
=(x^2+y^2+2xy)(x^2+y^2-2xy)
=(x+y)^2(x-y)^2
（4）x²-2xy+y²-9
=(x-y)^2-3^2
=(x-y+3)(x-y-3)
（5）x（x-1）+(x-1)²
=(x-1)(x+x-1)
=(X-1)(2x-1)
（6）(x²-1)²+6（1-X²）+9
=(X^2-1)-6(X^2-1)+9
(x^2-1-3)^2
=(X^2-4)^2.
=(X+2)^2(X-2)^2

Answer 4