Question

请问 这几题怎么做 因式分解

x(x^2-xy)-(4x^2-4xy) (a^2+2ab)^2+2(a^2+2ab)b^2+b^4 （x+y）^3-(x-y)^2(x+y)

Answer 1

(1)原式=x^2(x-y)-4x(x-y)
=(x-y)(x^2-4x)
=x(x-y)(x-4)
(2)可以看出三个部分组成一个完全平方式，所以，
原式=(a^2+2ab+b^2)^2
=[(a+b)^2]^2
=(a+b)^4
(3)原式=(x+y)[(x+y)^2-(x-y)^2]
=(x+y)(x+y+x-y)(x+y-x+y) {此步利用了平方差公式}
=4xy(x+y)

Answer 2

x(x²-xy)-(4x²-4xy)
=x²(x-y)-4x(x-y)
=(x-y)(x²-4x)
=x(x-y)(x-4)

(a²+2ab)²+2(a²+2ab)b²+b^4
=(a²+2ab)²+2(a²+2ab)b²+(b²)²
=(a²+2ab+b²)²
=(a+b)^4

(x+y)³-(x-y)²(x+y)=(x+y)[(x+y)²-(x-y)²]
=(x+y)(x+y+x-y)(x+y-x+y)
=4xy(x+y)

追问

对吗

追答

对

追问

m-m^5
199^2
58^2+84×58+42^2
真么写
我数学学的不好
麻烦了

追答

m-m^5=m(1-m^4)
=m(1+m²)(1-m²)
=n(1+m²)(1+m)(1-m)

199²=(200-1)²
=200²-2×200×1+1²
=40000-400+1
=39601

58²+84×58+42²=58²+2×42×58+42²
=(58+42)²
=100²
=10000
实际上就是反复应用平方差公式和和的平方公式