Evaluate (x^2+5)^2+5

${(x^{2} + 5)}^{2} + 5$

Step 1

Simplify each term.

Rewrite ${(x^{2} + 5)}^{2}$ as $(x^{2} + 5) (x^{2} + 5)$ .

$(x^{2} + 5) (x^{2} + 5) + 5$

Expand $(x^{2} + 5) (x^{2} + 5)$ using the FOIL Method.

Apply the distributive property.

$x^{2} (x^{2} + 5) + 5 (x^{2} + 5) + 5$

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot 5 + 5 (x^{2} + 5) + 5$

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot 5 + 5 x^{2} + 5 \cdot 5 + 5$

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.

$x^{2 + 2} + x^{2} \cdot 5 + 5 x^{2} + 5 \cdot 5 + 5$

Add $2$ and $2$ .

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

Move $5$ to the left of $x^{2}$ .

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

Multiply $5$ by $5$ .

$x^{4} + 5 x^{2} + 5 x^{2} + 25 + 5$

Add $5 x^{2}$ and $5 x^{2}$ .

$x^{4} + 10 x^{2} + 25 + 5$

Step 2

Add $25$ and $5$ .

$x^{4} + 10 x^{2} + 30$