Find the Product (6v^2+2v-9)(4-5v)

$(6 v^{2} + 2 v - 9) (4 - 5 v)$

Expand $(6 v^{2} + 2 v - 9) (4 - 5 v)$ by multiplying each term in the first expression by each term in the second expression.

$6 v^{2} \cdot 4 + 6 v^{2} (- 5 v) + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Simplify terms.

Simplify each term.

Multiply $4$ by $6$ .

$24 v^{2} + 6 v^{2} (- 5 v) + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Rewrite using the commutative property of multiplication.

$24 v^{2} + 6 \cdot - 5 v^{2} v + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Multiply $v^{2}$ by $v$ by adding the exponents.

Move $v$ .

$24 v^{2} + 6 \cdot - 5 (v \cdot v^{2}) + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Multiply $v$ by $v^{2}$ .

Raise $v$ to the power of $1$ .

$24 v^{2} + 6 \cdot - 5 (v^{1} v^{2}) + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$24 v^{2} + 6 \cdot - 5 v^{1 + 2} + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Add $1$ and $2$ .

$24 v^{2} + 6 \cdot - 5 v^{3} + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Multiply $6$ by $- 5$ .

$24 v^{2} - 30 v^{3} + 2 v \cdot 4 + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Multiply $4$ by $2$ .

$24 v^{2} - 30 v^{3} + 8 v + 2 v (- 5 v) - 9 \cdot 4 - 9 (- 5 v)$

Rewrite using the commutative property of multiplication.

$24 v^{2} - 30 v^{3} + 8 v + 2 \cdot - 5 v \cdot v - 9 \cdot 4 - 9 (- 5 v)$

Multiply $v$ by $v$ by adding the exponents.

Move $v$ .

$24 v^{2} - 30 v^{3} + 8 v + 2 \cdot - 5 (v \cdot v) - 9 \cdot 4 - 9 (- 5 v)$

Multiply $v$ by $v$ .

$24 v^{2} - 30 v^{3} + 8 v + 2 \cdot - 5 v^{2} - 9 \cdot 4 - 9 (- 5 v)$

Multiply $2$ by $- 5$ .

$24 v^{2} - 30 v^{3} + 8 v - 10 v^{2} - 9 \cdot 4 - 9 (- 5 v)$

Multiply $- 9$ by $4$ .

$24 v^{2} - 30 v^{3} + 8 v - 10 v^{2} - 36 - 9 (- 5 v)$

Multiply $- 5$ by $- 9$ .

$24 v^{2} - 30 v^{3} + 8 v - 10 v^{2} - 36 + 45 v$

Simplify by adding terms.

Subtract $10 v^{2}$ from $24 v^{2}$ .

$14 v^{2} - 30 v^{3} + 8 v - 36 + 45 v$

Add $8 v$ and $45 v$ .

$14 v^{2} - 30 v^{3} + 53 v - 36$