Question

1.把下列各式因式分解：

Answer 1

1.
x^2y^2-121
=(xy)^2-11^2
=(xy+11)(xy-11)
2.
1-y^4
=(1+y^2)(1-y^2)
=(1+y^2)(1+y)(1-y)
3.
(x+y)^2-4(x-y)^2
=(x+y)^2-[2(x-y)]^2
=(x+y+2x-2y)(x+y-2x+2y)
=(3x-y)(3y-x)
4.
(1+3x)^2-0.01x^2
=(1+3x)^2-(0.1x)^2
=(1+3x+0.1x)(1+3x-0.1x)
=(1+3.1x)(1+2.9x)
5.
25x^2y^2-x^2(x+y)^2
=(5xy)^2-[x(x+y)]^2
=[5xy+x(x+y)][5xy-x(x+y)]
=(5xy+x^2+xy)(5xy-x^2-xy)
=(x^2+6xy)(4xy-x^2)
=x^2(x+6y)(4y-x)