Đáp án+Giải thích các bước giải:
`61.`
`a) (x+2)(x+3)(x+4)(x+5) - 24`
`=[(x+2)(x+5)][(x+3)(x+4)] -24`
`= (x^2 + 7x + 10)(x^2 + 7x + 12) - 24`
`=[(x^2 + 7x +11)-1][(x^2 + 7x +11)-1]-24`
`=(x^2 + 7x +11)^2 -1 -24`
`=(x^2 + 7x +11)^2 - 25`
`=(x^2 + 7x +11-5)(x^2 + 7x + 11 + 5)`
`=(x^2 + 7x + 6)(x^2 +7x +16)`
`b) (4x+1)(12x-1)(3x+2)(x+1)-4`
`=[(4x+1)(3x+2)][(12x-1)(x+1)]-4`
`=(12x^2 +11x +2)(12x^2 +11x -1) -4`
`=[(12x^2 + 11x +0,5) + 1,5][(12x^2 + 11x +0,5) -1,5] -4`
`= (12x^2 + 11x + 0,5)^2 - 2,25 - 4`
`= (12x^2 + 11x + 0,5)^2 - (25)/4`
`= (12x^2 +11x + 0,5 - 5/2)(12x^2 +11x + 0,5 + 5/2)`
`=(12x^2 + 11x -2)(12x^2 + 11x + 3)`
`c) 4(x+5)(x+6)(x+10)(x+12) - 3x^2`
`=4[(x+5)(x+12)][(x+6)(x+10)] - 3x^2`
`=4(x^2 + 17x + 60)(x^2 + 16x + 60) - 3x^2`
Đặt `t = x^2 + 17x + 60`, khi đó biểu thức trên trở thành:
`4t(t-x) - 3x^2`
`=4t^2 - 4tx - 3x^2`
`=4t^2 + 2tx - 6tx - 3x^2`
`= 2t(2t+x)-3x(2t+x)`
`=(2t-3x)(2t+x)`
`=[2(x^2 + 17x +60)-3x][2(x^2 +17x +60) +x]`
`=(2x^2 + 34x + 120 - 3x)(2x^2 + 34x + 120 +x)`
`= (2x^2 +31x +120)(2x^2 +35x +120)`
