Algebra Examples

${(x + 3)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by $3$ .

$x^{3} + 9 x^{2} + 3 x \cdot 3^{2} + 3^{3}$

Step 2.2

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 2.2.1

Move $3^{2}$ .

$x^{3} + 9 x^{2} + 3^{2} \cdot 3 x + 3^{3}$

Step 2.2.2

Multiply $3^{2}$ by $3$ .

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Step 2.2.2.1

Raise $3$ to the power of $1$ .

$x^{3} + 9 x^{2} + 3^{2} \cdot 3^{1} x + 3^{3}$

Step 2.2.2.2

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

$x^{3} + 9 x^{2} + 3^{2 + 1} x + 3^{3}$

Step 2.2.3

Add $2$ and $1$ .

$x^{3} + 9 x^{2} + 3^{3} x + 3^{3}$

Step 2.3

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

$x^{3} + 9 x^{2} + 27 x + 3^{3}$

Step 2.4

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

$x^{3} + 9 x^{2} + 27 x + 27$