Question

express the following polynomial in expanded form and simplify completely.
\\p(x) = (x + 4)^4\\
\\p(x) =\\

Explanation:

Apply the Binomial Theorem for exponent 4

$$ (a + b)^4 = \binom{4}{0}a^4 + \binom{4}{1}a^3b + \binom{4}{2}a^2b^2 + \binom{4}{3}ab^3 + \binom{4}{4}b^4 $$

$$ \binom{4}{0}=1, \quad \binom{4}{1}=4, \quad \binom{4}{2}=6, \quad \binom{4}{3}=4, \quad \binom{4}{4}=1 $$

Substitute x and 4 into the expansion

$$
LATEXBLOCK0
$$

Simplify the coefficients

$$ p(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 $$

Answer:

Express the following polynomial in expanded form and simplify completely.
\(p(x) = (x + 4)^4\)

\(p(x) =\) <blank>\(x^4 + 16x^3 + 96x^2 + 256x + 256\)</blank>