Question

因式分解 1.4m的2次方-(m+n)的2次方 2.4x的3次方y+4x的2次方y的2次方+xy的3次方

3.5a的2次方b(x-y)的3次方-30ab的2次方（y-x）的平方
4.（a-b）的3次方-（a-b）
5.（x的2次方+y的2次方）的2次方=4x的2次方y的2次方
6.x的2次方-2xy+y的2次方-9

Answer 1

1.
4m²-(m+n)²=[2m+(m+n)][2m-(m+n)]=(3m+n)(m-n)
2.
4x³y+4x²y²+xy³=xy(4x²+4xy+y²)=xy(2x+y)²
3.
5a²b(x-y)³-30ab²(y-x)²
=5a²b(x-y)³-30ab²(x-y)²
=5ab(x-y)²[a(x-y)-6b]
=5ab(x-y)²(ax-ay-6b)
4.
(a-b)³-(a-b)
=(a-b)[(a-b)²-1]
=(a-b)(a-b+1)(a-b-1)
5.
(x²+y²)²-4x²y²
=(x²+y²+2xy)(x²+y²-2xy)
=(x+y)²(x-y)²
6.
x²-2xy+y²-9
=(x-y)²-9
=(x-y+3)(x-y-3)

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Answer 2

4m^2-(m+n)^2
=(2m+m+n)(2m-m-n)
=(3m+n)(m-n)

4x^3y+4x^2y^2+xy^3
=xy(4x^2+4xy+y^2)
=xy(2x+y)^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-6b)

（a-b）^3-（a-b）
=(a-b)[(a-b)^2-1]
=(a-b)(a-b+1)(a-b-1)

（x^2+y^2）^2=4x^2y^2
（x^2+y^2）^2-4x^2y^2=0
(x^2-y^2)^2=0
x^2-y^2=0
x=±y

x^2-2xy+y^2-9
=(x-y)^2-9
=(x-y+3)(x-y-3)