Solve (8d+6c^3)(6c^3-8d)

$$( 8 d + 6 c ^ { 3 } ) ( 6 c ^ { 3 } - 8 d )$$

Evaluate

$$36c^{6}-64d^{2}$$

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}.

$$\left(6c^{3}\right)^{2}-\left(8d\right)^{2}$$

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

$$6^{2}\left(c^{3}\right)^{2}-\left(8d\right)^{2}$$

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

$$6^{2}c^{6}-\left(8d\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36c^{6}-\left(8d\right)^{2}$$

Expand \left(8d\right)^{2}.

$$36c^{6}-8^{2}d^{2}$$

Calculate 8 to the power of 2 and get 64.

$$36c^{6}-64d^{2}$$

Expand

$$36c^{6}-64d^{2}$$

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}.

$$\left(6c^{3}\right)^{2}-\left(8d\right)^{2}$$

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

$$6^{2}\left(c^{3}\right)^{2}-\left(8d\right)^{2}$$

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

$$6^{2}c^{6}-\left(8d\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36c^{6}-\left(8d\right)^{2}$$

Expand \left(8d\right)^{2}.

$$36c^{6}-8^{2}d^{2}$$

Calculate 8 to the power of 2 and get 64.

$$36c^{6}-64d^{2}$$