1.x²(y-4)-(y-4)
=(x^2-1)(y-4)
=(x+1)(x-1)(y-4)
2.2x²-32
=2(x^2-16)
=2(x+4)(x-4)
3.已知a+b=8且a²-b²=48.则a-3b=
a+b=8
a^2-b^2=48
(a+b)(a-b)=48
a-b=6
a+b=8
a=8-b
把a=8-b代入a-b=6
8-b-b=6
8-2b=6
b=1
把b=1代入a-b=6
a-1=6
a=7
a-3b=7-3*1=4
4.x²-4y²
=(x+2y)(x-2y)
5.-x²+x²y²
=-x^2(1-y^2)
=-x^2(1+y)(1-y)
6.a²(a-b)+b²(b-a)
=(a^2-b^2)(a-b)
=(a+b)(a-b)^2
7.(a+b)²-(a-b)²
=(a+b+a-b)(a+b-a+b)
=2a(2b)
=4ab
8.4x²-5
题目是否有误?
9.x²-16
=(x+4)(x-4)
10.x^3+x²y-xy²-y^3
=x^2(x+y)-y^2(x+y)
=(x+y)^2(x-y)
11.(5m²+3n²）²-（3m²+5n²）²
=(5m^2+3n^2+3m^2+5n^2)(5m^2+3n^2-3m^2-5n^2)
=(8m^2+8n^2)(2m^2-2n^2)
=8(m^2+n^2)*2(m+n)(m-n)
=16(m+n)(m-n)(m^2+n^2)