Precalculus Examples

$x^{2} - y^{2} + n x + n y$

Step 1

Regroup terms.

$x^{2} - y^{2} + n x + n y$

Step 2

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

$(x + y) (x - y) + n x + n y$

Step 3

Factor $n$ out of $n x + n y$ .

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Step 3.1

Factor $n$ out of $n x$ .

$(x + y) (x - y) + n (x) + n y$

Step 3.2

Factor $n$ out of $n y$ .

$(x + y) (x - y) + n (x) + n (y)$

Step 3.3

Factor $n$ out of $n (x) + n (y)$ .

$(x + y) (x - y) + n (x + y)$

Step 4

Factor $x + y$ out of $(x + y) (x - y) + n (x + y)$ .

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Step 4.1

Factor $x + y$ out of $n (x + y)$ .

$(x + y) (x - y) + (x + y) n$

Step 4.2

Factor $x + y$ out of $(x + y) (x - y) + (x + y) n$ .

$(x + y) (x - y + n)$