Simplify (x+4)^4

${(x + 4)}^{4}$

Step 1

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot 4 + 6 x^{2} \cdot 4^{2} + 4 x \cdot 4^{3} + 4^{4}$

Step 2

Simplify each term.

Multiply $4$ by $4$ .

$x^{4} + 16 x^{3} + 6 x^{2} \cdot 4^{2} + 4 x \cdot 4^{3} + 4^{4}$

Raise $4$ to the power of $2$ .

$x^{4} + 16 x^{3} + 6 x^{2} \cdot 16 + 4 x \cdot 4^{3} + 4^{4}$

Multiply $16$ by $6$ .

$x^{4} + 16 x^{3} + 96 x^{2} + 4 x \cdot 4^{3} + 4^{4}$

Multiply $4$ by $4^{3}$ by adding the exponents.

Move $4^{3}$ .

$x^{4} + 16 x^{3} + 96 x^{2} + 4^{3} \cdot 4 x + 4^{4}$

Multiply $4^{3}$ by $4$ .

Raise $4$ to the power of $1$ .

$x^{4} + 16 x^{3} + 96 x^{2} + 4^{3} \cdot 4^{1} x + 4^{4}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} + 16 x^{3} + 96 x^{2} + 4^{3 + 1} x + 4^{4}$

Add $3$ and $1$ .

$x^{4} + 16 x^{3} + 96 x^{2} + 4^{4} x + 4^{4}$

Raise $4$ to the power of $4$ .

$x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 4^{4}$

Raise $4$ to the power of $4$ .

$x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 256$