Expand the Trigonometric Expression (4-5u)(4+5u)

$(4 - 5 u) (4 + 5 u)$

Step 1

Expand $(4 - 5 u) (4 + 5 u)$ using the FOIL Method.

Apply the distributive property.

$4 (4 + 5 u) - 5 u (4 + 5 u)$

Apply the distributive property.

$4 \cdot 4 + 4 (5 u) - 5 u (4 + 5 u)$

Apply the distributive property.

$4 \cdot 4 + 4 (5 u) - 5 u \cdot 4 - 5 u (5 u)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (5 u) - 5 u \cdot 4 - 5 u (5 u)$

Multiply $5$ by $4$ .

$16 + 20 u - 5 u \cdot 4 - 5 u (5 u)$

Multiply $4$ by $- 5$ .

$16 + 20 u - 20 u - 5 u (5 u)$

Rewrite using the commutative property of multiplication.

$16 + 20 u - 20 u - 5 \cdot 5 u \cdot u$

Multiply $u$ by $u$ by adding the exponents.

Move $u$ .

$16 + 20 u - 20 u - 5 \cdot 5 (u \cdot u)$

Multiply $u$ by $u$ .

$16 + 20 u - 20 u - 5 \cdot 5 u^{2}$

Multiply $- 5$ by $5$ .

$16 + 20 u - 20 u - 25 u^{2}$

Subtract $20 u$ from $20 u$ .

$16 + 0 - 25 u^{2}$

Add $16$ and $0$ .

$16 - 25 u^{2}$