Question

用配方法分解因式：(要过程）帮帮忙

x^2+2x-3
2x^2-7x+6
3x^2y^2-10xy+7
-y^2+20y-96

Answer 1

x^2+2x-3
=x^2+2x+1-1-3
=(x+1)^2-4
=(x+1-2)(x+1+2)
=(x-1)(x+3)

2x^2-7x+6
=2(x^2-7x/2+3)
=2(x^2-7x/2+49/16-49/16+3)
=2[(x-7/4)^2-1/16]
=2(x-7/4+1/4)(x-7/4-1/4)
=2(x-3/2)(x-2)
=(2x-3)(x-2)

3x^2y^2-10xy+7
=3(x^2y^2-10xy/3+7/3)
=3(x^2y^2-10xy/3+25/9-25/9+7/3)
=3[(xy-5/3)^2-4/9]
=3(xy-5/3-2/3)(xy-5/3+2/3)
=3(xy-7/3)(xy-1)
=(3xy-7)(xy-1)

-y^2+20y-96
=-(y^2-20y+96)
=-(y^2-20y+100-100+96)
=-[(y-10)^2-4]
=-(y-10-2)(y-10+2)
=-(y-12)(y-8)

Answer 2

x^2+2x-3
=x²+2x+1-4
=(x+1)²-4
=(x+1-2)(x+1+2)
=(x-1)(x+3)

2x^2-7x+6
=2x²-8x+8+x-2
=2(x-2)²+x-2
=(x-2)(2x-4+1)
=(x-2)(2x-3)

3x^2y^2-10xy+7
=3x²y²-3xy-7xy+7
=3xy(xy-1)-7(xy-1)
=(xy-1)(3xy-7)

-y^2+20y-96
=-y²+20y-100+4
=4-(y-10)²
=(2-y+10)(2+y-10)
=(12-y)(y-8)