Solve (2c^{2}d^3)^2+(-4cd^5)(6c^3d)

$$( 2 c ^ { 2 } d ^ { 3 } ) ^ { 2 } + ( - 4 c d ^ { 5 } ) ( 6 c ^ { 3 } d )$$

Evaluate

$$-20c^{4}d^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(2c^{2}d^{3}\right)^{2}-4c^{4}d^{5}\times 6d$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\left(2c^{2}d^{3}\right)^{2}-4c^{4}d^{6}\times 6$$

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

$$2^{2}\left(c^{2}\right)^{2}\left(d^{3}\right)^{2}-4c^{4}d^{6}\times 6$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2^{2}c^{4}\left(d^{3}\right)^{2}-4c^{4}d^{6}\times 6$$

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

$$2^{2}c^{4}d^{6}-4c^{4}d^{6}\times 6$$

Calculate 2 to the power of 2 and get 4.

$$4c^{4}d^{6}-4c^{4}d^{6}\times 6$$

Multiply -4 and 6 to get -24.

$$4c^{4}d^{6}-24c^{4}d^{6}$$

Combine 4c^{4}d^{6} and -24c^{4}d^{6} to get -20c^{4}d^{6}.

$$-20c^{4}d^{6}$$

Expand

$$-20c^{4}d^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(2c^{2}d^{3}\right)^{2}-4c^{4}d^{5}\times 6d$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\left(2c^{2}d^{3}\right)^{2}-4c^{4}d^{6}\times 6$$

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

$$2^{2}\left(c^{2}\right)^{2}\left(d^{3}\right)^{2}-4c^{4}d^{6}\times 6$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2^{2}c^{4}\left(d^{3}\right)^{2}-4c^{4}d^{6}\times 6$$

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

$$2^{2}c^{4}d^{6}-4c^{4}d^{6}\times 6$$

Calculate 2 to the power of 2 and get 4.

$$4c^{4}d^{6}-4c^{4}d^{6}\times 6$$

Multiply -4 and 6 to get -24.

$$4c^{4}d^{6}-24c^{4}d^{6}$$

Combine 4c^{4}d^{6} and -24c^{4}d^{6} to get -20c^{4}d^{6}.

$$-20c^{4}d^{6}$$