Basic Math Examples

$\frac{20 p^{9} + 15 p^{5}}{5 p}$

Step 1

Simplify terms.

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Step 1.1

Factor $5 p^{5}$ out of $20 p^{9} + 15 p^{5}$ .

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Step 1.1.1

Factor $5 p^{5}$ out of $20 p^{9}$ .

$\frac{5 p^{5} (4 p^{4}) + 15 p^{5}}{5 p}$

Step 1.1.2

Factor $5 p^{5}$ out of $15 p^{5}$ .

$\frac{5 p^{5} (4 p^{4}) + 5 p^{5} (3)}{5 p}$

Step 1.1.3

Factor $5 p^{5}$ out of $5 p^{5} (4 p^{4}) + 5 p^{5} (3)$ .

$\frac{5 p^{5} (4 p^{4} + 3)}{5 p}$

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

Cancel the common factor.

$\frac{5 p^{5} (4 p^{4} + 3)}{5 p}$

Step 1.2.2

Rewrite the expression.

$\frac{p^{5} (4 p^{4} + 3)}{p}$

Step 1.3

Cancel the common factor of $p^{5}$ and $p$ .

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Step 1.3.1

Factor $p$ out of $p^{5} (4 p^{4} + 3)$ .

$\frac{p (p^{4} (4 p^{4} + 3))}{p}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

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

$\frac{p (p^{4} (4 p^{4} + 3))}{p^{1}}$

Step 1.3.2.2

Factor $p$ out of $p^{1}$ .

$\frac{p (p^{4} (4 p^{4} + 3))}{p \cdot 1}$

Step 1.3.2.3

Cancel the common factor.

$\frac{p (p^{4} (4 p^{4} + 3))}{p \cdot 1}$

Step 1.3.2.4

Rewrite the expression.

$\frac{p^{4} (4 p^{4} + 3)}{1}$

Step 1.3.2.5

Divide $p^{4} (4 p^{4} + 3)$ by $1$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Reorder.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$4 p^{4} p^{4} + p^{4} \cdot 3$

Step 1.5.2

Move $3$ to the left of $p^{4}$ .

$4 p^{4} p^{4} + 3 \cdot p^{4}$

Step 2

Multiply $p^{4}$ by $p^{4}$ by adding the exponents.

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Step 2.1

Move $p^{4}$ .

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

Step 2.2

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

$4 p^{4 + 4} + 3 \cdot p^{4}$

Step 2.3

Add $4$ and $4$ .

$4 p^{8} + 3 \cdot p^{4}$

$4 p^{8} + 3 p^{4}$