Simplify (2r+5)(2r-5)

$(2 r + 5) (2 r - 5)$

Step 1

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

Apply the distributive property.

$2 r (2 r - 5) + 5 (2 r - 5)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

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

Multiply $r$ by $r$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 5$ by $2$ .

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

Multiply $2$ by $5$ .

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

Multiply $5$ by $- 5$ .

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

Add $- 10 r$ and $10 r$ .

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

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

$4 r^{2} - 25$