Find the Product (y^x-5)(y^x+5)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$y^{x} y^{x} + y^{x} \cdot 5 - 5 y^{x} - 5 \cdot 5$

Step 2

Simplify terms.

Combine the opposite terms in $y^{x} y^{x} + y^{x} \cdot 5 - 5 y^{x} - 5 \cdot 5$ .

Reorder the factors in the terms $y^{x} \cdot 5$ and $- 5 y^{x}$ .

$y^{x} y^{x} + 5 y^{x} - 5 y^{x} - 5 \cdot 5$

Subtract $5 y^{x}$ from $5 y^{x}$ .

$y^{x} y^{x} + 0 - 5 \cdot 5$

Add $y^{x} y^{x}$ and $0$ .

$y^{x} y^{x} - 5 \cdot 5$

Simplify each term.

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

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

$y^{x + x} - 5 \cdot 5$

Add $x$ and $x$ .

$y^{2 x} - 5 \cdot 5$

Multiply $- 5$ by $5$ .

$y^{2 x} - 25$