Factor 16ax+4x^2+16a^2

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

Step 1

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

Factor $4$ out of $16 a x$ .

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

Factor $4$ out of $4 x^{2}$ .

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

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

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

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

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

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

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

Step 2

Factor using the perfect square rule.

Rearrange terms.

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

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

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

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

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

Rewrite the polynomial.

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

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

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