Simplify (5x)^2+(5x^2-5)^2

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

Simplify each term.

Apply the product rule to $5 x$ .

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

Raise $5$ to the power of $2$ .

$25 x^{2} + {(5 x^{2} - 5)}^{2}$

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

$25 x^{2} + (5 x^{2} - 5) (5 x^{2} - 5)$

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

Apply the distributive property.

$25 x^{2} + 5 x^{2} (5 x^{2} - 5) - 5 (5 x^{2} - 5)$

Apply the distributive property.

$25 x^{2} + 5 x^{2} (5 x^{2}) + 5 x^{2} \cdot - 5 - 5 (5 x^{2} - 5)$

Apply the distributive property.

$25 x^{2} + 5 x^{2} (5 x^{2}) + 5 x^{2} \cdot - 5 - 5 (5 x^{2}) - 5 \cdot - 5$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$25 x^{2} + 5 \cdot 5 x^{2} x^{2} + 5 x^{2} \cdot - 5 - 5 (5 x^{2}) - 5 \cdot - 5$

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

Move $x^{2}$ .

$25 x^{2} + 5 \cdot 5 (x^{2} x^{2}) + 5 x^{2} \cdot - 5 - 5 (5 x^{2}) - 5 \cdot - 5$

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

$25 x^{2} + 5 \cdot 5 x^{2 + 2} + 5 x^{2} \cdot - 5 - 5 (5 x^{2}) - 5 \cdot - 5$

Add $2$ and $2$ .

$25 x^{2} + 5 \cdot 5 x^{4} + 5 x^{2} \cdot - 5 - 5 (5 x^{2}) - 5 \cdot - 5$

Multiply $5$ by $5$ .

$25 x^{2} + 25 x^{4} + 5 x^{2} \cdot - 5 - 5 (5 x^{2}) - 5 \cdot - 5$

Multiply $- 5$ by $5$ .

$25 x^{2} + 25 x^{4} - 25 x^{2} - 5 (5 x^{2}) - 5 \cdot - 5$

Multiply $5$ by $- 5$ .

$25 x^{2} + 25 x^{4} - 25 x^{2} - 25 x^{2} - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

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

Subtract $25 x^{2}$ from $- 25 x^{2}$ .

$25 x^{2} + 25 x^{4} - 50 x^{2} + 25$

Subtract $50 x^{2}$ from $25 x^{2}$ .

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