Simplify (r-2t)(r+2t)

$(r - 2 t) (r + 2 t)$

Step 1

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

Apply the distributive property.

$r (r + 2 t) - 2 t (r + 2 t)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $r \cdot r + r (2 t) - 2 t r - 2 t (2 t)$ .

Reorder the factors in the terms $r (2 t)$ and $- 2 t r$ .

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

Subtract $2 r t$ from $2 r t$ .

$r \cdot r + 0 - 2 t (2 t)$

Add $r \cdot r$ and $0$ .

$r \cdot r - 2 t (2 t)$

Simplify each term.

Multiply $r$ by $r$ .

$r^{2} - 2 t (2 t)$

Rewrite using the commutative property of multiplication.

$r^{2} - 2 \cdot 2 t \cdot t$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$r^{2} - 2 \cdot 2 (t \cdot t)$

Multiply $t$ by $t$ .

$r^{2} - 2 \cdot 2 t^{2}$

Multiply $- 2$ by $2$ .

$r^{2} - 4 t^{2}$