Expand the Trigonometric Expression (-2h+9)(9h-2)

$(- 2 h + 9) (9 h - 2)$

Step 1

Expand $(- 2 h + 9) (9 h - 2)$ using the FOIL Method.

Apply the distributive property.

$- 2 h (9 h - 2) + 9 (9 h - 2)$

Apply the distributive property.

$- 2 h (9 h) - 2 h \cdot - 2 + 9 (9 h - 2)$

Apply the distributive property.

$- 2 h (9 h) - 2 h \cdot - 2 + 9 (9 h) + 9 \cdot - 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 2 \cdot 9 h \cdot h - 2 h \cdot - 2 + 9 (9 h) + 9 \cdot - 2$

Multiply $h$ by $h$ by adding the exponents.

Move $h$ .

$- 2 \cdot 9 (h \cdot h) - 2 h \cdot - 2 + 9 (9 h) + 9 \cdot - 2$

Multiply $h$ by $h$ .

$- 2 \cdot 9 h^{2} - 2 h \cdot - 2 + 9 (9 h) + 9 \cdot - 2$

Multiply $- 2$ by $9$ .

$- 18 h^{2} - 2 h \cdot - 2 + 9 (9 h) + 9 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$- 18 h^{2} + 4 h + 9 (9 h) + 9 \cdot - 2$

Multiply $9$ by $9$ .

$- 18 h^{2} + 4 h + 81 h + 9 \cdot - 2$

Multiply $9$ by $- 2$ .

$- 18 h^{2} + 4 h + 81 h - 18$

Add $4 h$ and $81 h$ .

$- 18 h^{2} + 85 h - 18$