Finite Math Examples

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

Step 1

Rewrite ${(x^{2} - 25)}^{2}$ as $(x^{2} - 25) (x^{2} - 25)$ .

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

Step 2

Expand $(x^{2} - 25) (x^{2} - 25)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

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

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

Step 3.1.1.2

Add $2$ and $2$ .

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

Step 3.1.2

Move $- 25$ to the left of $x^{2}$ .

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

Step 3.1.3

Multiply $- 25$ by $- 25$ .

$x^{4} - 25 x^{2} - 25 x^{2} + 625$

Step 3.2

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

$x^{4} - 50 x^{2} + 625$