Solve 5m^3n*(-3n)^2+(-mn)*(-6mn)^2

$$5 m ^ { 3 } n \cdot ( - 3 n ) ^ { 2 } + ( - m n ) \cdot ( - 6 m n ) ^ { 2 }$$

Evaluate

$$9\left(mn\right)^{3}$$

Solution Steps

Expand \left(-3n\right)^{2}.

$$5m^{3}n\left(-3\right)^{2}n^{2}+\left(-m\right)n\left(-6mn\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$5m^{3}n\times 9n^{2}+\left(-m\right)n\left(-6mn\right)^{2}$$

Multiply 5 and 9 to get 45.

$$45m^{3}nn^{2}+\left(-m\right)n\left(-6mn\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$45m^{3}n^{3}+\left(-m\right)n\left(-6mn\right)^{2}$$

Expand \left(-6mn\right)^{2}.

$$45m^{3}n^{3}+\left(-m\right)n\left(-6\right)^{2}m^{2}n^{2}$$

Calculate -6 to the power of 2 and get 36.

$$45m^{3}n^{3}+\left(-m\right)n\times 36m^{2}n^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$45m^{3}n^{3}+\left(-m\right)n^{3}\times 36m^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$45m^{3}n^{3}-m^{3}n^{3}\times 36$$

Multiply -1 and 36 to get -36.

$$45m^{3}n^{3}-36m^{3}n^{3}$$

Combine 45m^{3}n^{3} and -36m^{3}n^{3} to get 9m^{3}n^{3}.

$$9m^{3}n^{3}$$

Expand

$$9\left(mn\right)^{3}$$

Solution Steps

Expand \left(-3n\right)^{2}.

$$5m^{3}n\left(-3\right)^{2}n^{2}+\left(-m\right)n\left(-6mn\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$5m^{3}n\times 9n^{2}+\left(-m\right)n\left(-6mn\right)^{2}$$

Multiply 5 and 9 to get 45.

$$45m^{3}nn^{2}+\left(-m\right)n\left(-6mn\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$45m^{3}n^{3}+\left(-m\right)n\left(-6mn\right)^{2}$$

Expand \left(-6mn\right)^{2}.

$$45m^{3}n^{3}+\left(-m\right)n\left(-6\right)^{2}m^{2}n^{2}$$

Calculate -6 to the power of 2 and get 36.

$$45m^{3}n^{3}+\left(-m\right)n\times 36m^{2}n^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$45m^{3}n^{3}+\left(-m\right)n^{3}\times 36m^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$45m^{3}n^{3}-m^{3}n^{3}\times 36$$

Multiply -1 and 36 to get -36.

$$45m^{3}n^{3}-36m^{3}n^{3}$$

Combine 45m^{3}n^{3} and -36m^{3}n^{3} to get 9m^{3}n^{3}.

$$9m^{3}n^{3}$$