Expand the Trigonometric Expression (9+m)(-m+9)

$(9 + m) (- m + 9)$

Step 1

Expand $(9 + m) (- m + 9)$ using the FOIL Method.

Apply the distributive property.

$9 (- m + 9) + m (- m + 9)$

Apply the distributive property.

$9 (- m) + 9 \cdot 9 + m (- m + 9)$

Apply the distributive property.

$9 (- m) + 9 \cdot 9 + m (- m) + m \cdot 9$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 1$ by $9$ .

$- 9 m + 9 \cdot 9 + m (- m) + m \cdot 9$

Multiply $9$ by $9$ .

$- 9 m + 81 + m (- m) + m \cdot 9$

Rewrite using the commutative property of multiplication.

$- 9 m + 81 - m \cdot m + m \cdot 9$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$- 9 m + 81 - (m \cdot m) + m \cdot 9$

Multiply $m$ by $m$ .

$- 9 m + 81 - m^{2} + m \cdot 9$

Move $9$ to the left of $m$ .

$- 9 m + 81 - m^{2} + 9 m$

Add $- 9 m$ and $9 m$ .

$81 - m^{2} + 0$

Add $81$ and $0$ .

$- m^{2} + 81$