Trigonometry Examples

$p^{2} - 4 r^{2} + 4 p^{3} + 8 p^{2} r$

Step 1

Regroup terms.

$p^{2} - 4 r^{2} + 4 p^{3} + 8 p^{2} r$

Step 2

Rewrite $4 r^{2}$ as ${(2 r)}^{2}$ .

$p^{2} - {(2 r)}^{2} + 4 p^{3} + 8 p^{2} r$

Step 3

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

$(p + 2 r) (p - (2 r)) + 4 p^{3} + 8 p^{2} r$

Step 4

Multiply $2$ by $- 1$ .

$(p + 2 r) (p - 2 r) + 4 p^{3} + 8 p^{2} r$

Step 5

Factor $4 p^{2}$ out of $4 p^{3} + 8 p^{2} r$ .

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Step 5.1

Factor $4 p^{2}$ out of $4 p^{3}$ .

$(p + 2 r) (p - 2 r) + 4 p^{2} (p) + 8 p^{2} r$

Step 5.2

Factor $4 p^{2}$ out of $8 p^{2} r$ .

$(p + 2 r) (p - 2 r) + 4 p^{2} (p) + 4 p^{2} (2 r)$

Step 5.3

Factor $4 p^{2}$ out of $4 p^{2} (p) + 4 p^{2} (2 r)$ .

$(p + 2 r) (p - 2 r) + 4 p^{2} (p + 2 r)$

Step 6

Factor $p + 2 r$ out of $(p + 2 r) (p - 2 r) + 4 p^{2} (p + 2 r)$ .

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Step 6.1

Factor $p + 2 r$ out of $4 p^{2} (p + 2 r)$ .

$(p + 2 r) (p - 2 r) + (p + 2 r) (4 p^{2})$

Step 6.2

Factor $p + 2 r$ out of $(p + 2 r) (p - 2 r) + (p + 2 r) (4 p^{2})$ .

$(p + 2 r) (p - 2 r + 4 p^{2})$