Show that $2-x-x^2=(2+x)(1-x)$. Find each binomial expansion $(2+x)^5$ and $(1-x)^5$ up to the

Question

Show that $2-x-x^2=(2+x)(1-x)$. Find each binomial expansion $(2+x)^5$ and $(1-x)^5$ up to the $x^2$ term. Hence find the coefficient of $x^2$ in $(2-x-x^2)^5$.

Accepted Answer

(a) $32+80x+80x^2+\cdots$, (b) $1-5x+10x^2+\cdots$; (c) Coefficient $0$.

Binomial Theorem

Binomial Theorem