Algebra Examples

$p (x) = {(x + 3)}^{4}$

Step 1

Write $p (x) = {(x + 3)}^{4}$ as an equation.

$y = {(x + 3)}^{4}$

Step 2

Simplify ${(x + 3)}^{4}$ .

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Step 2.1

Use the Binomial Theorem.

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $3$ by $4$ .

$y = x^{4} + 12 x^{3} + 6 x^{2} \cdot 3^{2} + 4 x \cdot 3^{3} + 3^{4}$

Step 2.2.2

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

$y = x^{4} + 12 x^{3} + 6 x^{2} \cdot 9 + 4 x \cdot 3^{3} + 3^{4}$

Step 2.2.3

Multiply $9$ by $6$ .

$y = x^{4} + 12 x^{3} + 54 x^{2} + 4 x \cdot 3^{3} + 3^{4}$

Step 2.2.4

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

$y = x^{4} + 12 x^{3} + 54 x^{2} + 4 x \cdot 27 + 3^{4}$

Step 2.2.5

Multiply $27$ by $4$ .

$y = x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 3^{4}$

Step 2.2.6

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

$y = x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81$