Pre-Algebra Examples

${(x^{2} + y)}^{2} - 10 (x^{2} + y) + 16$

Step 1

Let $u = x^{2} + y$ . Substitute $u$ for all occurrences of $x^{2} + y$ .

$u^{2} - 10 u + 16$

Step 2

Factor $u^{2} - 10 u + 16$ using the AC method.

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Step 2.1

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 $16$ and whose sum is $- 10$ .

$- 8, - 2$

Step 2.2

Write the factored form using these integers.

$(u - 8) (u - 2)$

Step 3

Replace all occurrences of $u$ with $x^{2} + y$ .

$(x^{2} + y - 8) (x^{2} + y - 2)$