Algebra Examples

$a n^{2} + c n^{2} - a p + a p^{2} - c p + c p^{2}$

Step 1

Regroup terms.

$a n^{2} - a p + a p^{2} + c n^{2} - c p + c p^{2}$

Step 2

Factor $a$ out of $a n^{2} - a p + a p^{2}$ .

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Step 2.1

Factor $a$ out of $a n^{2}$ .

$a (n^{2}) - a p + a p^{2} + c n^{2} - c p + c p^{2}$

Step 2.2

Factor $a$ out of $- a p$ .

$a (n^{2}) + a (- 1 p) + a p^{2} + c n^{2} - c p + c p^{2}$

Step 2.3

Factor $a$ out of $a p^{2}$ .

$a (n^{2}) + a (- 1 p) + a (p^{2}) + c n^{2} - c p + c p^{2}$

Step 2.4

Factor $a$ out of $a (n^{2}) + a (- 1 p)$ .

$a (n^{2} - 1 p) + a (p^{2}) + c n^{2} - c p + c p^{2}$

Step 2.5

Factor $a$ out of $a (n^{2} - 1 p) + a (p^{2})$ .

$a (n^{2} - 1 p + p^{2}) + c n^{2} - c p + c p^{2}$

Step 3

Rewrite $- 1 p$ as $- p$ .

$a (n^{2} - p + p^{2}) + c n^{2} - c p + c p^{2}$

Step 4

Factor $c$ out of $c n^{2} - c p + c p^{2}$ .

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Step 4.1

Factor $c$ out of $c n^{2}$ .

$a (n^{2} - p + p^{2}) + c (n^{2}) - c p + c p^{2}$

Step 4.2

Factor $c$ out of $- c p$ .

$a (n^{2} - p + p^{2}) + c (n^{2}) + c (- 1 p) + c p^{2}$

Step 4.3

Factor $c$ out of $c p^{2}$ .

$a (n^{2} - p + p^{2}) + c (n^{2}) + c (- 1 p) + c (p^{2})$

Step 4.4

Factor $c$ out of $c (n^{2}) + c (- 1 p)$ .

$a (n^{2} - p + p^{2}) + c (n^{2} - 1 p) + c (p^{2})$

Step 4.5

Factor $c$ out of $c (n^{2} - 1 p) + c (p^{2})$ .

$a (n^{2} - p + p^{2}) + c (n^{2} - 1 p + p^{2})$

Step 5

Rewrite $- 1 p$ as $- p$ .

$a (n^{2} - p + p^{2}) + c (n^{2} - p + p^{2})$

Step 6

Factor $n^{2} - p + p^{2}$ out of $a (n^{2} - p + p^{2}) + c (n^{2} - p + p^{2})$ .

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Step 6.1

Factor $n^{2} - p + p^{2}$ out of $a (n^{2} - p + p^{2})$ .

$(n^{2} - p + p^{2}) a + c (n^{2} - p + p^{2})$

Step 6.2

Factor $n^{2} - p + p^{2}$ out of $c (n^{2} - p + p^{2})$ .

$(n^{2} - p + p^{2}) a + (n^{2} - p + p^{2}) c$

Step 6.3

Factor $n^{2} - p + p^{2}$ out of $(n^{2} - p + p^{2}) a + (n^{2} - p + p^{2}) c$ .

$(n^{2} - p + p^{2}) (a + c)$