Đáp án:
`c)(12x²+11x+3)(12x²+11x-2)`
`d)(x+8)(2x+15)(2x²+35x+120)`
Giải thích các bước giải:
`c)(4x+1)(12x-1)(3x+2)(x+1)-4`
`=[(4x+1)(3x+2)][(12x-1)(x+1)]-4`
`=(12x²+8x+3x+2)(12x²+12x-x-1)-4`
`=(12x²+11x+2)(12x²+11x-1)-4`
Đặt `12x²+11x-1=a` khi đó phương trình trở thành:
`(a+3)a-4`
`=a²+3a-4`
`=a²+4a-a-4`
`=a(a+4)-(a+4)`
`=(a+4)(a-1)`
`=(12x²+11x-1+4)(12x²+11x-1-1)`
`=(12x²+11x+3)(12x²+11x-2)`
`d)4(x+5)(x+6)(x+10)(x+12)-3x²`
`=4[(x+5)(x+12)][(x+6)(x+10)]-3x²`
`=4(x²+12x+5x+60)(x²+10x+6x+60)-3x²`
`=4(x²+17x+60)(x²+16x+60)-3x²`
Đặt `x²+16x+60=a` khi đó phương trình trở thành:
`4(a+x)a-3x²`
`=4a²+4ax-3x²`
`=4a²-2ax+6ax-3x²`
`=2a(2a-x)+3x(2a-x)`
`=(2a-x)(2a+3x)`
`=[2(x²+16x+60)-x][2(x²+16x+60)+3x]`
`=(2x²+32x+120-x)(2x²+32x+120+3x)`
`=(2x²+31x+120)(2x²+35x+120)`
`=(2x²+16x+15x+120)(2x²+35x+120)`
`=[2x(x+8)+15(x+8)](2x²+35x+120)`
`=(x+8)(2x+15)(2x²+35x+120)`
