Question

数学~~~~~~~~~

因式分解：
4x²-y²+4x-2y
x³+x²y-xy²-y²
9-9x²+4y²-12y
4x²-4xy+y²-2x+y-2

Answer 1

1
4x²-y²+4x-2y=（2x+1）的平方减（y+1）的平方=（2x+1-y-1）（2x+1+y+1）=（2x-y））（2x+1+y+1）
2
x³+x²y-xy²-y²=x²（x+1）-y²（x+1）=（x+1）（x²-y²）=（x+y）（x+1）的平方
3
9-9x²+4y²-12y=-9x²+（2y-3）的平方=（2y-3-3x）（2y-3+3x）
4
4x²-4xy+y²-2x+y-2 =(2x-y)^2-(2x-y)-2=(2x-y-2)(2x-y+1)

Answer 2

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

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

9-9x^2+4y^2-12y
=4y^2-12y+9-9x^2
=(2y-3)^2-9x^2
=(2y-3+3x)(2y-3-3x)

4x^2-4xy+y^2-2x+y-2
=(2x-y)^2-(2x-y)-2
=(2x-y+1)(2x-y-2)

Answer 3

4x²-y²+4x-2y
=(2x-y)(2x+y)+2(2x-y)
=(2x-y)(2x+y+2)

x³+x²y-xy²-y²
=x^2(x+1)-y^2(x+1)
=(x+1)(x+y)(x-y)

9-9x²+4y²-12y
=(2y-3)^2-9x^2
=(2y-3+3x)(2y-3-3x)

4x²-4xy+y²-2x+y-2
=(2x-y)^2-(2x-y)-2
=(2x-y-2)(2x-y+1)