Simplify (5a+4)(5a-4)

$(5 a + 4) (5 a - 4)$

Step 1

Expand $(5 a + 4) (5 a - 4)$ using the FOIL Method.

Apply the distributive property.

$5 a (5 a - 4) + 4 (5 a - 4)$

Apply the distributive property.

$5 a (5 a) + 5 a \cdot - 4 + 4 (5 a - 4)$

Apply the distributive property.

$5 a (5 a) + 5 a \cdot - 4 + 4 (5 a) + 4 \cdot - 4$

Step 2

Simplify terms.

Combine the opposite terms in $5 a (5 a) + 5 a \cdot - 4 + 4 (5 a) + 4 \cdot - 4$ .

Reorder the factors in the terms $5 a \cdot - 4$ and $4 (5 a)$ .

$5 a (5 a) - 4 \cdot 5 a + 4 \cdot 5 a + 4 \cdot - 4$

Add $- 4 \cdot 5 a$ and $4 \cdot 5 a$ .

$5 a (5 a) + 0 + 4 \cdot - 4$

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

$5 a (5 a) + 4 \cdot - 4$

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 a \cdot a + 4 \cdot - 4$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$5 \cdot 5 (a \cdot a) + 4 \cdot - 4$

Multiply $a$ by $a$ .

$5 \cdot 5 a^{2} + 4 \cdot - 4$

Multiply $5$ by $5$ .

$25 a^{2} + 4 \cdot - 4$

Multiply $4$ by $- 4$ .

$25 a^{2} - 16$