Solve (6m^3+9n)(6m^3-9n)

$$( 6 m ^ { 3 } + 9 n ) ( 6 m ^ { 3 } - 9 n )$$

Evaluate

$$36m^{6}-81n^{2}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(6m^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$6^{2}m^{6}-\left(9n\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36m^{6}-\left(9n\right)^{2}$$

Expand \left(9n\right)^{2}.

$$36m^{6}-9^{2}n^{2}$$

Calculate 9 to the power of 2 and get 81.

$$36m^{6}-81n^{2}$$

Expand

$$36m^{6}-81n^{2}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(6m^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$6^{2}m^{6}-\left(9n\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36m^{6}-\left(9n\right)^{2}$$

Expand \left(9n\right)^{2}.

$$36m^{6}-9^{2}n^{2}$$

Calculate 9 to the power of 2 and get 81.

$$36m^{6}-81n^{2}$$