Algebra Examples

${(x - 4)}^{2} + (x - 4)$

Step 1

Remove parentheses.

${(x - 4)}^{2} + x - 4$

Step 2

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

$u^{2} - 7 u + 12$

Step 3

Factor $u^{2} - 7 u + 12$ using the AC method.

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Step 3.1

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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Step 3.2

Write the factored form using these integers.

$(u - 4) (u - 3)$

Step 4

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

$(x - 4) (x - 3)$