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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $4$ by $4$ .

$16 a^{2} + 4 a \cdot - 5 + 5 (4 a) + 5 \cdot - 5$

Multiply $- 5$ by $4$ .

$16 a^{2} - 20 a + 5 (4 a) + 5 \cdot - 5$

Multiply $4$ by $5$ .

$16 a^{2} - 20 a + 20 a + 5 \cdot - 5$

Multiply $5$ by $- 5$ .

$16 a^{2} - 20 a + 20 a - 25$

Add $- 20 a$ and $20 a$ .

$16 a^{2} + 0 - 25$

Add $16 a^{2}$ and $0$ .

$16 a^{2} - 25$