Simplify (x^2+7)^2

${(x^{2} + 7)}^{2}$

Step 1

Rewrite ${(x^{2} + 7)}^{2}$ as $(x^{2} + 7) (x^{2} + 7)$ .

$(x^{2} + 7) (x^{2} + 7)$

Step 2

Expand $(x^{2} + 7) (x^{2} + 7)$ using the FOIL Method.

Apply the distributive property.

$x^{2} (x^{2} + 7) + 7 (x^{2} + 7)$

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot 7 + 7 (x^{2} + 7)$

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

Step 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.

$x^{2 + 2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

Add $2$ and $2$ .

$x^{4} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

Move $7$ to the left of $x^{2}$ .

$x^{4} + 7 \cdot x^{2} + 7 x^{2} + 7 \cdot 7$

Multiply $7$ by $7$ .

$x^{4} + 7 x^{2} + 7 x^{2} + 49$

Add $7 x^{2}$ and $7 x^{2}$ .

$x^{4} + 14 x^{2} + 49$