Basic Math Examples

$b^{2} - 16 - 6 b + 24$

Step 1

Regroup terms.

$- 6 b + b^{2} - 16 + 24$

Step 2

Add $- 16$ and $24$ .

$- 6 b + b^{2} + 8$

Step 3

Let $u = b$ . Substitute $u$ for all occurrences of $b$ .

$- 6 u + u^{2} + 8$

Step 4

Factor $- 6 u + u^{2} + 8$ using the AC method.

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Step 4.1

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 $- 6$ .

$- 4, - 2$

Step 4.2

Write the factored form using these integers.

$(u - 4) (u - 2)$

Step 5

Replace all occurrences of $u$ with $b$ .

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