Basic Math Examples

$\frac{15 p^{3} + 18 p^{2}}{3}$

Step 1

Simplify terms.

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Step 1.1

Factor $3 p^{2}$ out of $15 p^{3} + 18 p^{2}$ .

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Step 1.1.1

Factor $3 p^{2}$ out of $15 p^{3}$ .

$\frac{3 p^{2} (5 p) + 18 p^{2}}{3}$

Step 1.1.2

Factor $3 p^{2}$ out of $18 p^{2}$ .

$\frac{3 p^{2} (5 p) + 3 p^{2} (6)}{3}$

Step 1.1.3

Factor $3 p^{2}$ out of $3 p^{2} (5 p) + 3 p^{2} (6)$ .

$\frac{3 p^{2} (5 p + 6)}{3}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Cancel the common factor.

$\frac{3 p^{2} (5 p + 6)}{3}$

Step 1.2.2

Divide $p^{2} (5 p + 6)$ by $1$ .

$p^{2} (5 p + 6)$

Step 1.3

Apply the distributive property.

$p^{2} (5 p) + p^{2} \cdot 6$

Step 1.4

Reorder.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$5 p^{2} p + p^{2} \cdot 6$

Step 1.4.2

Move $6$ to the left of $p^{2}$ .

$5 p^{2} p + 6 \cdot p^{2}$

Step 2

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

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Step 2.1

Move $p$ .

$5 (p \cdot p^{2}) + 6 \cdot p^{2}$

Step 2.2

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

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Step 2.2.1

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

$5 (p^{1} p^{2}) + 6 \cdot p^{2}$

Step 2.2.2

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

$5 p^{1 + 2} + 6 \cdot p^{2}$

Step 2.3

Add $1$ and $2$ .

$5 p^{3} + 6 \cdot p^{2}$

$5 p^{3} + 6 p^{2}$