Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $5 x$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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Step 1.4.1

Apply the distributive property.

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

Step 1.4.2

Apply the distributive property.

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

Step 1.4.3

Apply the distributive property.

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

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Rewrite using the commutative property of multiplication.

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

Step 1.5.1.2

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

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Step 1.5.1.2.1

Move $x^{2}$ .

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

Step 1.5.1.2.2

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

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

Step 1.5.1.2.3

Add $2$ and $2$ .

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

Step 1.5.1.3

Multiply $5$ by $5$ .

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

Step 1.5.1.4

Multiply $- 5$ by $5$ .

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

Step 1.5.1.5

Multiply $5$ by $- 5$ .

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

Step 1.5.1.6

Multiply $- 5$ by $- 5$ .

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

Step 1.5.2

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

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

Step 2

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

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