Question

cho mình hỏi câu này ạ,mình cảm ơn.
x(x+1)^4 +x(x+1)^3 +x(x+1)^2 +(x+1)^2=(x+1)^5

Answer 1

Ý bạn là chứng minh

Ta có:

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

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

\(=\left(x+1\right)^3\left[x\left(x+1\right)+x+1\right]\)

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

\(=\left(x+1\right)^3\left(x+1\right)^2=\left(x+1\right)^5\)