Find the Product (100-x)(100+x)

$(100 - x) (100 + x)$

Step 1

Expand $(100 - x) (100 + x)$ using the FOIL Method.

Apply the distributive property.

$100 (100 + x) - x (100 + x)$

Apply the distributive property.

$100 \cdot 100 + 100 x - x (100 + x)$

Apply the distributive property.

$100 \cdot 100 + 100 x - x \cdot 100 - x \cdot x$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $100$ by $100$ .

$10000 + 100 x - x \cdot 100 - x \cdot x$

Multiply $100$ by $- 1$ .

$10000 + 100 x - 100 x - x \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$10000 + 100 x - 100 x - (x \cdot x)$

Multiply $x$ by $x$ .

$10000 + 100 x - 100 x - x^{2}$

Subtract $100 x$ from $100 x$ .

$10000 + 0 - x^{2}$

Add $10000$ and $0$ .

$10000 - x^{2}$