Question

Chứng minh rằng : \(x\left(x+1\right)^4+x\left(x+1\right)^3+x\left(x+1\right)^2+\left(x+1\right)^2=\left(x+1\right)^5\)

Giúp mình nhé !!! Mình cần gấp ! Thanks 

Answer 1

\(x\left(x+1\right)^4+x\left(x+1\right)^3+x\left(x+1\right)^2+\left(x+1\right)^2\)

\(=\left(x+1\right)^2\left[x\left(x+1\right)^2+x\left(x+1\right)+x+1\right]\)

\(=\left(x+1\right)^2\left[x\left(x+1\right)\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)\right]\)

\(=\left(x+1\right)^2\left\{\left(x+1\right)\left[x\left(x+1\right)+x+1\right]\right\}\)

\(=\left(x+1\right)^2\left\{\left(x+1\right)\left[x^2+x+x+1\right]\right\}\)

\(=\left(x+1\right)^2\left[\left(x+1\right)\left(x^2+2x+1\right)\right]\)

\(=\left(x+1\right)^2\cdot\left(x+1\right)^3\)

\(=\left(x+1\right)^5\left(đpcm\right)\)

Answer 2

thanks bonking