Finite Math Examples

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

Step 1

Expand $(x + 5) (x - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Combine the opposite terms in $x \cdot x + x \cdot - 5 + 5 x + 5 \cdot - 5$ .

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Step 2.1

Reorder the factors in the terms $x \cdot - 5$ and $5 x$ .

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

Step 2.2

Add $- 5 x$ and $5 x$ .

$x \cdot x + 0 + 5 \cdot - 5 - (x^{2} - 25)$

Step 2.3

Add $x \cdot x$ and $0$ .

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

Step 3

Simplify each term.

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Step 3.1

Multiply $x$ by $x$ .

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

Step 3.2

Multiply $5$ by $- 5$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $- 1$ by $- 25$ .

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

Step 6

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

$0 - 25 + 25$

Step 7

Subtract $25$ from $0$ .

$- 25 + 25$

Step 8

Add $- 25$ and $25$ .

$0$