Algebra Examples

$\frac{p - 5}{p + 3}$ , $p^{2} - 9$

Step 1

Multiply the expressions.

$\frac{p - 5}{p + 3} \cdot (p^{2} - 9)$

Step 2

Multiply $\frac{p - 5}{p + 3}$ by $p^{2} - 9$ .

$\frac{(p - 5) (p^{2} - 9)}{p + 3}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $9$ as $3^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = p$ and $b = 3$ .

$\frac{(p - 5) (p + 3) (p - 3)}{p + 3}$

Step 4

Cancel the common factor of $p + 3$ .

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Step 4.1

Cancel the common factor.

$\frac{(p - 5) (p + 3) (p - 3)}{p + 3}$

Step 4.2

Divide $(p - 5) (p - 3)$ by $1$ .

$(p - 5) (p - 3)$

Step 5

Expand $(p - 5) (p - 3)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$p (p - 3) - 5 (p - 3)$

Step 5.2

Apply the distributive property.

$p \cdot p + p \cdot - 3 - 5 (p - 3)$

Step 5.3

Apply the distributive property.

$p \cdot p + p \cdot - 3 - 5 p - 5 \cdot - 3$

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply $p$ by $p$ .

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

Step 6.1.2

Move $- 3$ to the left of $p$ .

$p^{2} - 3 \cdot p - 5 p - 5 \cdot - 3$

Step 6.1.3

Multiply $- 5$ by $- 3$ .

$p^{2} - 3 p - 5 p + 15$

Step 6.2

Subtract $5 p$ from $- 3 p$ .

$p^{2} - 8 p + 15$