Simplify (5x-8)(5x+8)

$(5 x - 8) (5 x + 8)$

Step 1

Expand $(5 x - 8) (5 x + 8)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x + 8) - 8 (5 x + 8)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 8 - 8 (5 x + 8)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot 8 - 8 (5 x) - 8 \cdot 8$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot 8 - 8 (5 x) - 8 \cdot 8$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot 8 - 8 (5 x) - 8 \cdot 8$

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x \cdot 8 - 8 (5 x) - 8 \cdot 8$

Multiply $5$ by $5$ .

$25 x^{2} + 5 x \cdot 8 - 8 (5 x) - 8 \cdot 8$

Multiply $8$ by $5$ .

$25 x^{2} + 40 x - 8 (5 x) - 8 \cdot 8$

Multiply $5$ by $- 8$ .

$25 x^{2} + 40 x - 40 x - 8 \cdot 8$

Multiply $- 8$ by $8$ .

$25 x^{2} + 40 x - 40 x - 64$

Subtract $40 x$ from $40 x$ .

$25 x^{2} + 0 - 64$

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

$25 x^{2} - 64$