Solve (2c-8d^2)*(2c+8d^2)

$$( 2 c - 8 d ^ { 2 } ) \cdot ( 2 c + 8 d ^ { 2 } )$$

Evaluate

$$4\left(c^{2}-16d^{4}\right)$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4c^{2}-\left(8d^{2}\right)^{2}$$

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

$$4c^{2}-8^{2}\left(d^{2}\right)^{2}$$

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

$$4c^{2}-8^{2}d^{4}$$

Calculate 8 to the power of 2 and get 64.

$$4c^{2}-64d^{4}$$

Expand

$$4c^{2}-64d^{4}$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4c^{2}-\left(8d^{2}\right)^{2}$$

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

$$4c^{2}-8^{2}\left(d^{2}\right)^{2}$$

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

$$4c^{2}-8^{2}d^{4}$$

Calculate 8 to the power of 2 and get 64.

$$4c^{2}-64d^{4}$$