Basic Math Examples

$\frac{w^{2} + 3 w - 28}{6 w^{2} - 96}$

Step 1

Factor $w^{2} + 3 w - 28$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 28$ and whose sum is $3$ .

$- 4, 7$

Step 1.2

Write the factored form using these integers.

$\frac{(w - 4) (w + 7)}{6 w^{2} - 96}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $6$ out of $6 w^{2} - 96$ .

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Step 2.1.1

Factor $6$ out of $6 w^{2}$ .

$\frac{(w - 4) (w + 7)}{6 (w^{2}) - 96}$

Step 2.1.2

Factor $6$ out of $- 96$ .

$\frac{(w - 4) (w + 7)}{6 w^{2} + 6 \cdot - 16}$

Step 2.1.3

Factor $6$ out of $6 w^{2} + 6 \cdot - 16$ .

$\frac{(w - 4) (w + 7)}{6 (w^{2} - 16)}$

Step 2.2

Rewrite $16$ as $4^{2}$ .

$\frac{(w - 4) (w + 7)}{6 (w^{2} - 4^{2})}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = w$ and $b = 4$ .

$\frac{(w - 4) (w + 7)}{6 (w + 4) (w - 4)}$

Step 3

Cancel the common factor of $w - 4$ .

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Step 3.1

Cancel the common factor.

$\frac{(w - 4) (w + 7)}{6 (w + 4) (w - 4)}$

Step 3.2

Rewrite the expression.

$\frac{w + 7}{6 (w + 4)}$