Expand the Trigonometric Expression (5n-5)(2+2n)

$(5 n - 5) (2 + 2 n)$

Step 1

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

Apply the distributive property.

$5 n (2 + 2 n) - 5 (2 + 2 n)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $5$ .

$10 n + 5 n (2 n) - 5 \cdot 2 - 5 (2 n)$

Rewrite using the commutative property of multiplication.

$10 n + 5 \cdot 2 n \cdot n - 5 \cdot 2 - 5 (2 n)$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$10 n + 5 \cdot 2 (n \cdot n) - 5 \cdot 2 - 5 (2 n)$

Multiply $n$ by $n$ .

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

Multiply $5$ by $2$ .

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

Multiply $- 5$ by $2$ .

$10 n + 10 n^{2} - 10 - 5 (2 n)$

Multiply $2$ by $- 5$ .

$10 n + 10 n^{2} - 10 - 10 n$

Subtract $10 n$ from $10 n$ .

$10 n^{2} - 10 + 0$

Add $10 n^{2}$ and $0$ .

$10 n^{2} - 10$