Basic Math Examples

$\frac{b^{2} - 2 b - 8}{b - 6} \cdot (b - 6)$

Step 1

Factor $b^{2} - 2 b - 8$ 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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Step 1.2

Write the factored form using these integers.

$\frac{(b - 4) (b + 2)}{b - 6} \cdot (b - 6)$

Step 2

Cancel the common factor of $b - 6$ .

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Step 2.1

Cancel the common factor.

$\frac{(b - 4) (b + 2)}{b - 6} \cdot (b - 6)$

Step 2.2

Rewrite the expression.

$(b - 4) (b + 2)$

Step 3

Expand $(b - 4) (b + 2)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$b (b + 2) - 4 (b + 2)$

Step 3.2

Apply the distributive property.

$b \cdot b + b \cdot 2 - 4 (b + 2)$

Step 3.3

Apply the distributive property.

$b \cdot b + b \cdot 2 - 4 b - 4 \cdot 2$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $b$ by $b$ .

$b^{2} + b \cdot 2 - 4 b - 4 \cdot 2$

Step 4.1.2

Move $2$ to the left of $b$ .

$b^{2} + 2 \cdot b - 4 b - 4 \cdot 2$

Step 4.1.3

Multiply $- 4$ by $2$ .

$b^{2} + 2 b - 4 b - 8$

Step 4.2

Subtract $4 b$ from $2 b$ .

$b^{2} - 2 b - 8$