Factor 4x^4+4+8x^2

$4 x^{4} + 4 + 8 x^{2}$

Step 1

Factor $4$ out of $4 x^{4} + 4 + 8 x^{2}$ .

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

$4 (x^{4}) + 4 + 8 x^{2}$

Factor $4$ out of $4$ .

$4 (x^{4}) + 4 (1) + 8 x^{2}$

Factor $4$ out of $8 x^{2}$ .

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

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

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

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

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

Step 2

Factor using the perfect square rule.

Rearrange terms.

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

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

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

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

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

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

$2 x^{2} = 2 \cdot x^{2} \cdot 1$

Rewrite the polynomial.

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

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

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