Question

4道初一因式分解

①4(x-y)²+4(y-x)+1
②3m(a-b)-9(b-a)²
③(a²+ab+b²)²-9a²b²
④(x²-5)²-8(x²-5)+16
3x(y-x)-6y(x-y)

Answer 1

第一个：[2(y-x)²-1]²
第二个：-[3(a-b)](m+b-a）
第三个：(a-b)²(a²+b²+4ab)
第四个：(x²-1)²

Answer 2

1.[2（x-y)-1]^2
2.3(a-b)*[m-3(a-b)]
3[(a+b)^2-(ab)^2]^2-9a^2*b^2=[(a+b)^2--(ab)^2+3*a*b]*[(a+b)^2--(ab)^2-3*a*b]
4.[(x^2-5)-4]^2

Answer 3

①4(x-y)²+4(y-x)+1
=4(x-y)²-4(x-y)+1
=[2(x-y)-1]²
=(2x-2y-1)²

②3m(a-b)-9(b-a)²
=3(a-b)(m-3a+3b)

③(a²+ab+b²)²-9a²b²
=(a²+ab+b²+3ab)(a²+ab+b²-3ab)
=(a²+4ab+b²)(a²-2ab+b²)
=(a²+4ab+b²)(a-b)²

④(x²-5)²-8(x²-5)+16
=(x²-5-4)²
=(x²-9)²
=(x-3)²(x+3)²

3x(y-x)-6y(x-y)
=3x(y-x)+6y(y-x)
=3(y-x)(x+2y)