Giải thích các bước giải:
`a,(48x^2+8x-1)(3x^2+5x+2)-4`
`=(48x^2+12x-4x-1)(3x^2+3x+2x+2)-4`
`=[12x(4x+1)-(4x+1)][3x(x+1)+2(x+1)]-4`
`=(12x-1)(4x+1)(3x+2)(x+1)-4`
`=[(12x-1)(x+1)][(4x+1)(3x+2)]-4`
`=(12x^2+11x-1)(12x^2+11x+2)-4` (1)
$\text{Đặt: $12x^2 + 11x - 1 = t$}$
(1) `=t(t+3)-4`
`=t^2+3t-4`
`=t^2-t+4t-4`
`=t(t-1)+4(t-1)`
`=(t+4)(t-1)` (2)
$\text{Thay $t=12x^2 + 11x - 1$ vào ta được:}$
(2) `=(12x^2+11x-1+4)(12x^2+11x-1-1)`
`=(12x^2+11x+3)(12x^2+11x-2)`
b/ `(12x-1)(6x-1)(4x-1)(3x-1)-330`
`=(12x-1)(3x-1)(6x-1)(4x-1)-330`
`=(36x^2-15x+1)(24x^2-10x+1)-330`
$=\dfrac{2}{3}.\dfrac{3}{2}(36x^2-15x+1)(24x^2-10x+1)-330$
$=\dfrac{2}{3}.(36x^2-15x+1)(36x^2-15x+\dfrac{3}{2})-330$ (3)
$\text{Đặt $36x^2-15x+1=t$}$
(3) $=\dfrac{2}{3}.t.(t+\dfrac{1}{2})-330$
$=\dfrac{2}{3}t^2+\dfrac{1}{3}t-330$
$=\dfrac{1}{3}.(2t^2+t-990)$
$=\dfrac{1}{3}.(2t^2-44t+45t-990)$
$=\dfrac{1}{3}.[2t(t-22)+45(t-22)]$
$=\dfrac{1}{3}.(t-22)(2t+45)$ (4)
$\text{Thay $t=36x^2-15x+1$ ta được:}$
(4) $=\dfrac{1}{3}.(34x^2-15x+1-22)[2(34x^2-15x+1)+45]$
$=\dfrac{1}{3}.(34x^2-15x-21)(68x^2-30x+47)$
Chúc bạn học tốt !!!
