Simplify (2a+5)(2a-5)

$(2 a + 5) (2 a - 5)$

Step 1

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

Apply the distributive property.

$2 a (2 a - 5) + 5 (2 a - 5)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 5$ by $2$ .

$4 a^{2} - 10 a + 5 (2 a) + 5 \cdot - 5$

Multiply $2$ by $5$ .

$4 a^{2} - 10 a + 10 a + 5 \cdot - 5$

Multiply $5$ by $- 5$ .

$4 a^{2} - 10 a + 10 a - 25$

Add $- 10 a$ and $10 a$ .

$4 a^{2} + 0 - 25$

Add $4 a^{2}$ and $0$ .

$4 a^{2} - 25$