Question

分解因式。每题5分。

x^2y^3-x^3y^2-xy
-4xy-4x^2-4y^2
2a^4b^2-4a^3b^2+10ab^4
ab-½(a^2+b^2)
16x-x^3
2(5m-17)^2-128(m-1)^2
5(m-n)^3+10(n-m)^5

Answer 1

解答：
(1)x^2y^3-x^3y^2-xy=xy(xy^2-x^2y-1)
(2)-4xy-4x^2-4y^2=-4(x^2+xy+y^2)
(3)2a^4b^2-4a^3b^2+10ab^4=2ab^2(a^3-2a^2+5b^3)
(4)ab-½(a^2+b^2)=-(a-b)^2/2
(5)16x-x^3=x(4+x)(4-x)
(6)2(5m-17)^2-128(m-1)^2=2[(5m-17)^2-64(m-1)^2]=2[(5m-17)+(8m-8)][(5m-7)-(8m-8)]
=2(13m-25)(1-3m)
(7)5(m-n)^3+10(n-m)^5=5(m0n)^3[1-2(m-n)^2]

Answer 2

x^2y^3-x^3y^2-xy=xy(xy²-x²y-1)

-4xy-4x^2-4y^2=-4(xy+x²+y²)

2a^4b^2-4a^3b^2+10ab^4=2ab(a³b-2a²b+5b³)

ab-½(a^2+b^2)=(2ab-a²-b²)/2=-(a²-2ab+b²)/2=-(a-b)²/2

16x-x^3=x(16-x²)=x(4-x)(4+x)

2(5m-17)^2-128(m-1)^2
=2[(5m-17)²-64(m-1)²]
=2(5m-17-8m+8)(5m-17+8m-8)
=2(-3m-9)(13m-25)
=-6(m+3)(13m-25)

5(m-n)^3+10(n-m)^5
=5(m-n)³-10(m-n)^5
=5(m-n)³[1-(m-n)²]
=5(m-n)³(1-m+n)(1+m-n)