Algebra Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $2 p$ .

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

Step 2.2

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

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

Step 2.3

Apply the product rule to $2 p$ .

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

Step 2.4

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

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

Step 2.5

Multiply $8$ by $4$ .

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

Step 2.6

Multiply $4$ by $32$ .

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

Step 2.7

Apply the product rule to $2 p$ .

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

Step 2.8

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

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

Step 2.9

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

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Step 2.9.1

Move $4^{2}$ .

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

Step 2.9.2

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

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Step 2.9.2.1

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

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

Step 2.9.2.2

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

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

Step 2.9.3

Add $2$ and $1$ .

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

Step 2.10

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

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

Step 2.11

Multiply $64$ by $6$ .

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

Step 2.12

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

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Step 2.12.1

Move $4^{3}$ .

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

Step 2.12.2

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

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Step 2.12.2.1

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

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

Step 2.12.2.2

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

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

Step 2.12.3

Add $3$ and $1$ .

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

Step 2.13

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

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

Step 2.14

Multiply $2$ by $256$ .

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

Step 2.15

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

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