Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Move $p^{2}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

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

Step 2.3

Add $2$ and $1$ .

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

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

Step 3

Multiply $q$ by $q$ by adding the exponents.

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Step 3.1

Move $q$ .

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

Step 3.2

Multiply $q$ by $q$ .

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

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

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $6$ .

$18 p^{3} q + 6 p q^{2} \cdot 4$

Step 4.2

Multiply $4$ by $6$ .

$18 p^{3} q + 24 p q^{2}$

$18 p^{3} q + 24 p q^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$