Simplify (5x-9)(5x+9)

$(5 x - 9) (5 x + 9)$

Step 1

Expand $(5 x - 9) (5 x + 9)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x + 9) - 9 (5 x + 9)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 9 - 9 (5 x + 9)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 9 - 9 (5 x) - 9 \cdot 9$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot 9 - 9 (5 x) - 9 \cdot 9$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot 9 - 9 (5 x) - 9 \cdot 9$

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x \cdot 9 - 9 (5 x) - 9 \cdot 9$

Multiply $5$ by $5$ .

$25 x^{2} + 5 x \cdot 9 - 9 (5 x) - 9 \cdot 9$

Multiply $9$ by $5$ .

$25 x^{2} + 45 x - 9 (5 x) - 9 \cdot 9$

Multiply $5$ by $- 9$ .

$25 x^{2} + 45 x - 45 x - 9 \cdot 9$

Multiply $- 9$ by $9$ .

$25 x^{2} + 45 x - 45 x - 81$

Subtract $45 x$ from $45 x$ .

$25 x^{2} + 0 - 81$

Add $25 x^{2}$ and $0$ .

$25 x^{2} - 81$