Let $P(x)=(1+x)^6(1-x)^4.$ Rewrite $P(x)$ using a power of $1-x^2$. Find the coefficient

Question

Let $P(x)=(1+x)^6(1-x)^4.$ Rewrite $P(x)$ using a power of $1-x^2$. Find the coefficient of $x^5$. Find the sum of all odd-power coefficients, and explain how that sum is compatible with your answer to part $2$.

Accepted Answer

(a) $(1-x^2)^4(1+x)^2$; (b) Coefficient $12$; (c) Odd-power coefficient sum $0$.

Binomial Theorem

Binomial Theorem

Solution:

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