Simplify 2(x^2+1)^2+3

$2 {(x^{2} + 1)}^{2} + 3$

Step 1

Simplify each term.

Rewrite ${(x^{2} + 1)}^{2}$ as $(x^{2} + 1) (x^{2} + 1)$ .

$2 ((x^{2} + 1) (x^{2} + 1)) + 3$

Expand $(x^{2} + 1) (x^{2} + 1)$ using the FOIL Method.

Apply the distributive property.

$2 (x^{2} (x^{2} + 1) + 1 (x^{2} + 1)) + 3$

Apply the distributive property.

$2 (x^{2} x^{2} + x^{2} \cdot 1 + 1 (x^{2} + 1)) + 3$

Apply the distributive property.

$2 (x^{2} x^{2} + x^{2} \cdot 1 + 1 x^{2} + 1 \cdot 1) + 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 (x^{2 + 2} + x^{2} \cdot 1 + 1 x^{2} + 1 \cdot 1) + 3$

Add $2$ and $2$ .

$2 (x^{4} + x^{2} \cdot 1 + 1 x^{2} + 1 \cdot 1) + 3$

Multiply $x^{2}$ by $1$ .

$2 (x^{4} + x^{2} + 1 x^{2} + 1 \cdot 1) + 3$

Multiply $x^{2}$ by $1$ .

$2 (x^{4} + x^{2} + x^{2} + 1 \cdot 1) + 3$

Multiply $1$ by $1$ .

$2 (x^{4} + x^{2} + x^{2} + 1) + 3$

Add $x^{2}$ and $x^{2}$ .

$2 (x^{4} + 2 x^{2} + 1) + 3$

Apply the distributive property.

$2 x^{4} + 2 (2 x^{2}) + 2 \cdot 1 + 3$

Simplify.

Multiply $2$ by $2$ .

$2 x^{4} + 4 x^{2} + 2 \cdot 1 + 3$

Multiply $2$ by $1$ .

$2 x^{4} + 4 x^{2} + 2 + 3$

Step 2

Add $2$ and $3$ .

$2 x^{4} + 4 x^{2} + 5$