Solve -2(1-4a^2)^2

$$- 2 ( 1 - 4 a ^ { 2 } ) ^ { 2 }$$

Expand

$$-32a^{4}+16a^{2}-2$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(1-4a^{2}\right)^{2}.

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

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

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

Use the distributive property to multiply -2 by 1-8a^{2}+16a^{4}.

$$-2+16a^{2}-32a^{4}$$

Evaluate

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

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(1-4a^{2}\right)^{2}.

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

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

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

Use the distributive property to multiply -2 by 1-8a^{2}+16a^{4}.

$$-2+16a^{2}-32a^{4}$$