Question

(x+1)(x+2)(x+3)(x+4)-24

Answer 1

\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-24\)

\(=\left(x^2+4x+x+4\right)\left(x^2+3x+2x+6\right)-24\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

đặt \(\left(x^2+5x+4\right)=a\)

\(=a\left(a+2\right)-24\)

\(=\left(a^2+2a+1\right)-25\)

\(=\left(a-4\right)\left(a+6\right)\)

bạn thay \(a=\left(x^2+5x+4\right)\) vào là được nha

Answer 2

(x+1)(x+2)(x+3)(x+4)-24

= \(x^4+10x^3+35x^2+50x\)

= \(x\left(x+5\right)\left(x^2+5x+10\right)\)