Đáp án:
`1)(x²+x+6)(x²-3x+6)`
`2)(x²-6x-8)(x²-3x-8)`
Giải thích các bước giải:
`1)(x-1)(x+2)(x+3)(x-6)+32x²`
`=[(x-1)(x-6)][(x+2)(x+3)]+32x²`
`=(x²-6x-x+6)(x²+3x+2x+6)+32x²`
`=(x²-7x+6)(x²+5x+6)+32x²`
Đặt `x²+6=a`,khi đó ta được:
`(a-7x)(a+5x)+32x²`
`=a²+5ax-7ax-35x²+32x²`
`=a²-2ax-3x²`
`=a²+ax-3ax-3x²`
`=a(a+x)-3x(a+x)`
`=(a+x)(a-3x)`
`=(x²+6+x)(x²+6-3x)`
`=(x²+x+6)(x²-3x+6)`
`2)(x+1)(x-4)(x+2)(x-8)+4x²`
`=[(x+1)(x-8)][(x-4)(x+2)]+4x²`
`=(x²-8x+x-8)(x²+2x-4x-8)+4x²`
`=(x²-7x-8)(x²-2x-8)+4x²`
Đặt `x²-8=a`, khi đó ta được:
`(a-7x)(a-2x)+4x²`
`=a²-2ax-7ax+14x²+4x²`
`=a²-9ax+18x²`
`=a²-6ax-3ax+18x²`
`=a(a-6x)-3x(a-6x)`
`=(a-6x)(a-3x)`
`=(x²-8-6x)(x²-8-3x)`
`=(x²-6x-8)(x²-3x-8)`
