Question

因式分解求解答

Answer 1

8、
1、
xy+x-y-1
=x(y+1)-(y+1)
=(x-1)(y+1)
2、
x²-y²-x+y
=(x+y)(x-y)-(x-y)
=(x+y-1)(x-y)
3、
3ax-3ay-xy+y²
=3a(x-y)-y(x-y)
=(3a-y)(x-y)
4、
4xy+1-4x²-y²
=1-(4x²-4xy+y²)
=1-(2x-y)²
=(1+2x-y)(1-2x+y)
5、
8x³+4x²-2x-1
=4x²(2x+1)-(2x+1)
=(4x²-1)(2x+1)
=(2x+1)(2x-1)(2x+1)
=(2x-1)(2x+1)²
6、
x²(x+1)-y(xy+x)
=x³+x²-xy²-xy
=x(x²-y²)+x(x-y)
=x(x-y)(x+y)+x(x-y)
=x(x-y)(2x+y)
7、
x^5+x^4+x³+x²+x+1
=x³(x²+x+1)+x²+x+1
=(x³+1)(x²+x+1)
=(x+1)(x²-x+1)(x²+x+1)
8、
x²-4mx+8mn-4n²
=x²-4n²-4m(x-2n)
=(x+2n)(x-2n)-4m(x-2n)
=(x+2n-4m)(x-2n)
9、
ab(x²+y²)+xy(a²+b²)
=abx²+aby²+xya²+xyb²
=ax(bx+ay)+by(ay+bx)
=(ax+by)(ay+bx)