Expand the Trigonometric Expression (2p+4)^4

${(2 p + 4)}^{4}$

Use the Binomial Theorem.

${(2 p)}^{4} + 4 {(2 p)}^{3} \cdot 4 + 6 {(2 p)}^{2} \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

Simplify each term.

Apply the product rule to $2 p$ .

$2^{4} p^{4} + 4 {(2 p)}^{3} \cdot 4 + 6 {(2 p)}^{2} \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

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

$16 p^{4} + 4 {(2 p)}^{3} \cdot 4 + 6 {(2 p)}^{2} \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

Apply the product rule to $2 p$ .

$16 p^{4} + 4 (2^{3} p^{3}) \cdot 4 + 6 {(2 p)}^{2} \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

Raise $2$ to the power of $3$ .

$16 p^{4} + 4 (8 p^{3}) \cdot 4 + 6 {(2 p)}^{2} \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

Multiply $8$ by $4$ .

$16 p^{4} + 32 p^{3} \cdot 4 + 6 {(2 p)}^{2} \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

Multiply $4$ by $32$ .

$16 p^{4} + 128 p^{3} + 6 {(2 p)}^{2} \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

Apply the product rule to $2 p$ .

$16 p^{4} + 128 p^{3} + 6 (2^{2} p^{2}) \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

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

$16 p^{4} + 128 p^{3} + 6 (4 p^{2}) \cdot 4^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

Multiply $4$ by $4^{2}$ by adding the exponents.

Move $4^{2}$ .

$16 p^{4} + 128 p^{3} + 6 (4^{2} \cdot 4 p^{2}) + 4 (2 p) \cdot 4^{3} + 4^{4}$

Multiply $4^{2}$ by $4$ .

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

$16 p^{4} + 128 p^{3} + 6 (4^{2} \cdot 4^{1} p^{2}) + 4 (2 p) \cdot 4^{3} + 4^{4}$

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

$16 p^{4} + 128 p^{3} + 6 (4^{2 + 1} p^{2}) + 4 (2 p) \cdot 4^{3} + 4^{4}$

Add $2$ and $1$ .

$16 p^{4} + 128 p^{3} + 6 (4^{3} p^{2}) + 4 (2 p) \cdot 4^{3} + 4^{4}$

Raise $4$ to the power of $3$ .

$16 p^{4} + 128 p^{3} + 6 (64 p^{2}) + 4 (2 p) \cdot 4^{3} + 4^{4}$

Multiply $64$ by $6$ .

$16 p^{4} + 128 p^{3} + 384 p^{2} + 4 (2 p) \cdot 4^{3} + 4^{4}$

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

Move $4^{3}$ .

$16 p^{4} + 128 p^{3} + 384 p^{2} + 4^{3} \cdot 4 (2 p) + 4^{4}$

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

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

$16 p^{4} + 128 p^{3} + 384 p^{2} + 4^{3} \cdot 4^{1} (2 p) + 4^{4}$

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

$16 p^{4} + 128 p^{3} + 384 p^{2} + 4^{3 + 1} (2 p) + 4^{4}$

Add $3$ and $1$ .

$16 p^{4} + 128 p^{3} + 384 p^{2} + 4^{4} (2 p) + 4^{4}$

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

$16 p^{4} + 128 p^{3} + 384 p^{2} + 256 (2 p) + 4^{4}$

Multiply $2$ by $256$ .

$16 p^{4} + 128 p^{3} + 384 p^{2} + 512 p + 4^{4}$

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

$16 p^{4} + 128 p^{3} + 384 p^{2} + 512 p + 256$

Expand the Trigonometric Expression (2p+4)^4

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