Thích nhất bài này nè!
\(\left(x^2+8x+7\right)\left(x+3\right)\left(x+5\right)+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)(1)
Đặt \(x^2+8x+7=t\Rightarrow x^2+8x+15=t+8\)
Do đó \(\left(1\right)=t\left(t+8\right)+15=t^2+8t+15\)
\(=t^2+3t+5t+15=t\left(t+3\right)+5\left(t+3\right)=\left(t+3\right)\left(t+5\right)\)(*)
Vì \(t=x^2+8x+7\) nên :
\(\left(\text{*}\right)=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+2x+6x+12\right)\)
\(=\left(x^2+8x+10\right)\left[x\left(x+2\right)+6\left(x+2\right)\right]\)
\(=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)
Vậy...........
Chúc bạn học tốt!!!
(x2 + 8x + 7 )(x+3)(x+5) + 15
= (x2 + x + 7x + 7 )(x2 + 8x +15) + 15
= (x2 + x +7x + 7 )(x2 + 3x + 5x +15) + 15
= (x(x + 1) + 7(x + 1))(x(x + 3)+ 5(x + 3) + 15
= (x+1)(x+7)(x+5)(x+3) +15
