Solve (4k^2)^2-4(2k^2-2)(1+2k^2)

$$( 4 k ^ { 2 } ) ^ { 2 } - 4 ( 2 k ^ { 2 } - 2 ) ( 1 + 2 k ^ { 2 } )$$

Evaluate

$$8\left(k^{2}+1\right)$$

Solution Steps

Expand \left(4k^{2}\right)^{2}.

$$4^{2}\left(k^{2}\right)^{2}-4\left(2k^{2}-2\right)\left(1+2k^{2}\right)$$

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

$$4^{2}k^{4}-4\left(2k^{2}-2\right)\left(1+2k^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$16k^{4}-4\left(2k^{2}-2\right)\left(1+2k^{2}\right)$$

Use the distributive property to multiply -4 by 2k^{2}-2.

$$16k^{4}+\left(-8k^{2}+8\right)\left(1+2k^{2}\right)$$

Use the distributive property to multiply -8k^{2}+8 by 1+2k^{2} and combine like terms.

$$16k^{4}+8k^{2}-16k^{4}+8$$

Combine 16k^{4} and -16k^{4} to get 0.

$$8k^{2}+8$$

Expand

$$8k^{2}+8$$

Solution Steps

Expand \left(4k^{2}\right)^{2}.

$$4^{2}\left(k^{2}\right)^{2}-4\left(2k^{2}-2\right)\left(1+2k^{2}\right)$$

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

$$4^{2}k^{4}-4\left(2k^{2}-2\right)\left(1+2k^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$16k^{4}-4\left(2k^{2}-2\right)\left(1+2k^{2}\right)$$

Use the distributive property to multiply -4 by 2k^{2}-2.

$$16k^{4}+\left(-8k^{2}+8\right)\left(1+2k^{2}\right)$$

Use the distributive property to multiply -8k^{2}+8 by 1+2k^{2} and combine like terms.

$$16k^{4}+8k^{2}-16k^{4}+8$$

Combine 16k^{4} and -16k^{4} to get 0.

$$8k^{2}+8$$