Simplify (-6qr)(9q^2+4qr^2-7)

$(- 6 q r) (9 q^{2} + 4 q r^{2} - 7)$

Apply the distributive property.

$- 6 q r (9 q^{2}) - 6 q r (4 q r^{2}) - 6 q r \cdot - 7$

Simplify.

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

Move $q^{2}$ .

$- 6 (q^{2} q) r \cdot 9 - 6 q r (4 q r^{2}) - 6 q r \cdot - 7$

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

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

$- 6 (q^{2} q^{1}) r \cdot 9 - 6 q r (4 q r^{2}) - 6 q r \cdot - 7$

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

$- 6 q^{2 + 1} r \cdot 9 - 6 q r (4 q r^{2}) - 6 q r \cdot - 7$

Add $2$ and $1$ .

$- 6 q^{3} r \cdot 9 - 6 q r (4 q r^{2}) - 6 q r \cdot - 7$

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

$- 6 q^{3} r \cdot 9 - 6 (q \cdot q) r (4 r^{2}) - 6 q r \cdot - 7$

Multiply $q$ by $q$ .

$- 6 q^{3} r \cdot 9 - 6 q^{2} r (4 r^{2}) - 6 q r \cdot - 7$

Multiply $- 7$ by $- 6$ .

$- 6 q^{3} r \cdot 9 - 6 q^{2} r (4 r^{2}) + 42 q r$

Simplify each term.

Multiply $9$ by $- 6$ .

$- 54 q^{3} r - 6 q^{2} r (4 r^{2}) + 42 q r$

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

Move $r^{2}$ .

$- 54 q^{3} r - 6 q^{2} (r^{2} r) \cdot 4 + 42 q r$

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

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

$- 54 q^{3} r - 6 q^{2} (r^{2} r^{1}) \cdot 4 + 42 q r$

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

$- 54 q^{3} r - 6 q^{2} r^{2 + 1} \cdot 4 + 42 q r$

Add $2$ and $1$ .

$- 54 q^{3} r - 6 q^{2} r^{3} \cdot 4 + 42 q r$

Multiply $4$ by $- 6$ .

$- 54 q^{3} r - 24 q^{2} r^{3} + 42 q r$