Question

分解因式：3ax+4by+4ay+3bx

4x²-y²-4x+2y
1-x²+2xy-y²

Answer 1

3ax+4by+4ay+3bx=3x(a+b)+4y(a+b)=(a+b)(3x+4y)
4x²-y²-4x+2y=(2x-1)²-(y-1)²=(2x-1+y-1)(2x-1-y+1)=(2x+y-2)(2x-y)
1-x²+2xy-y²=1-(x-y)²=(1+x-y)(1-x+y)

Answer 2

3ax+4by+4ay+3bx
=(3ax+3bx)+(4ay+4by)
=3x(a+b)+4y(a+b)
=(a+b)(3x+4y)

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

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