Expand the Trigonometric Expression (7-2w)(7+2w)

$(7 - 2 w) (7 + 2 w)$

Step 1

Expand $(7 - 2 w) (7 + 2 w)$ using the FOIL Method.

Apply the distributive property.

$7 (7 + 2 w) - 2 w (7 + 2 w)$

Apply the distributive property.

$7 \cdot 7 + 7 (2 w) - 2 w (7 + 2 w)$

Apply the distributive property.

$7 \cdot 7 + 7 (2 w) - 2 w \cdot 7 - 2 w (2 w)$

Step 2

Simplify terms.

Combine the opposite terms in $7 \cdot 7 + 7 (2 w) - 2 w \cdot 7 - 2 w (2 w)$ .

Reorder the factors in the terms $7 (2 w)$ and $- 2 w \cdot 7$ .

$7 \cdot 7 + 2 \cdot 7 w - 2 \cdot 7 w - 2 w (2 w)$

Subtract $2 \cdot 7 w$ from $2 \cdot 7 w$ .

$7 \cdot 7 + 0 - 2 w (2 w)$

Add $7 \cdot 7$ and $0$ .

$7 \cdot 7 - 2 w (2 w)$

Simplify each term.

Multiply $7$ by $7$ .

$49 - 2 w (2 w)$

Rewrite using the commutative property of multiplication.

$49 - 2 \cdot 2 w \cdot w$

Multiply $w$ by $w$ by adding the exponents.

Move $w$ .

$49 - 2 \cdot 2 (w \cdot w)$

Multiply $w$ by $w$ .

$49 - 2 \cdot 2 w^{2}$

Multiply $- 2$ by $2$ .

$49 - 4 w^{2}$