Trigonometry Examples

$4 + 16 a + 16 a^{2}$

Step 1

Factor $4$ out of $4 + 16 a + 16 a^{2}$ .

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Step 1.1

Factor $4$ out of $4$ .

$4 (1) + 16 a + 16 a^{2}$

Step 1.2

Factor $4$ out of $16 a$ .

$4 (1) + 4 (4 a) + 16 a^{2}$

Step 1.3

Factor $4$ out of $16 a^{2}$ .

$4 (1) + 4 (4 a) + 4 (4 a^{2})$

Step 1.4

Factor $4$ out of $4 (1) + 4 (4 a)$ .

$4 (1 + 4 a) + 4 (4 a^{2})$

Step 1.5

Factor $4$ out of $4 (1 + 4 a) + 4 (4 a^{2})$ .

$4 (1 + 4 a + 4 a^{2})$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$4 (1^{2} + 4 a + 4 a^{2})$

Step 2.2

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

$4 (1^{2} + 4 a + {(2 a)}^{2})$

Step 2.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 a = 2 \cdot 1 \cdot (2 a)$

Step 2.4

Rewrite the polynomial.

$4 (1^{2} + 2 \cdot 1 \cdot (2 a) + {(2 a)}^{2})$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 1$ and $b = 2 a$ .

$4 {(1 + 2 a)}^{2}$