Simplify (5x-2)(5x+2)

$(5 x - 2) (5 x + 2)$

Step 1

Expand $(5 x - 2) (5 x + 2)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x + 2) - 2 (5 x + 2)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 2 - 2 (5 x + 2)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 2 - 2 (5 x) - 2 \cdot 2$

Step 2

Simplify terms.

Combine the opposite terms in $5 x (5 x) + 5 x \cdot 2 - 2 (5 x) - 2 \cdot 2$ .

Reorder the factors in the terms $5 x \cdot 2$ and $- 2 (5 x)$ .

$5 x (5 x) + 2 \cdot 5 x - 2 \cdot 5 x - 2 \cdot 2$

Subtract $2 \cdot 5 x$ from $2 \cdot 5 x$ .

$5 x (5 x) + 0 - 2 \cdot 2$

Add $5 x (5 x)$ and $0$ .

$5 x (5 x) - 2 \cdot 2$

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x - 2 \cdot 2$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) - 2 \cdot 2$

Multiply $x$ by $x$ .

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

Multiply $5$ by $5$ .

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

Multiply $- 2$ by $2$ .

$25 x^{2} - 4$