Algebra Examples

${(h + 3 k)}^{3}$

Step 1

Use the Binomial Theorem.

$h^{3} + 3 h^{2} (3 k) + 3 h {(3 k)}^{2} + {(3 k)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$h^{3} + 3 \cdot 3 h^{2} k + 3 h {(3 k)}^{2} + {(3 k)}^{3}$

Step 2.2

Multiply $3$ by $3$ .

$h^{3} + 9 h^{2} k + 3 h {(3 k)}^{2} + {(3 k)}^{3}$

Step 2.3

Apply the product rule to $3 k$ .

$h^{3} + 9 h^{2} k + 3 h (3^{2} k^{2}) + {(3 k)}^{3}$

Step 2.4

Rewrite using the commutative property of multiplication.

$h^{3} + 9 h^{2} k + 3 \cdot 3^{2} h k^{2} + {(3 k)}^{3}$

Step 2.5

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

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Step 2.5.1

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

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Step 2.5.1.1

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

$h^{3} + 9 h^{2} k + 3^{1} \cdot 3^{2} h k^{2} + {(3 k)}^{3}$

Step 2.5.1.2

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

$h^{3} + 9 h^{2} k + 3^{1 + 2} h k^{2} + {(3 k)}^{3}$

Step 2.5.2

Add $1$ and $2$ .

$h^{3} + 9 h^{2} k + 3^{3} h k^{2} + {(3 k)}^{3}$

Step 2.6

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

$h^{3} + 9 h^{2} k + 27 h k^{2} + {(3 k)}^{3}$

Step 2.7

Apply the product rule to $3 k$ .

$h^{3} + 9 h^{2} k + 27 h k^{2} + 3^{3} k^{3}$

Step 2.8

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

$h^{3} + 9 h^{2} k + 27 h k^{2} + 27 k^{3}$