Expand the Trigonometric Expression (5+z)^4

${(5 + z)}^{4}$

Step 1

Use the Binomial Theorem.

$5^{4} + 4 \cdot 5^{3} z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Step 2

Simplify each term.

Raise $5$ to the power of $4$ .

$625 + 4 \cdot 5^{3} z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Raise $5$ to the power of $3$ .

$625 + 4 \cdot 125 z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Multiply $4$ by $125$ .

$625 + 500 z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Raise $5$ to the power of $2$ .

$625 + 500 z + 6 \cdot 25 z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Multiply $6$ by $25$ .

$625 + 500 z + 150 z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Multiply $4$ by $5$ .

$625 + 500 z + 150 z^{2} + 20 z^{3} + z^{4}$