Solve (2a^{2})^{2}-(-3a^4)+(-3a^2)^2-20a^4

$$( 2 a ^ { 2 } ) ^ { 2 } - ( - 3 a ^ { 4 } ) + ( - 3 a ^ { 2 } ) ^ { 2 } - 20 a ^ { 4 }$$

Evaluate

$$-4a^{4}$$

Solution Steps

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

$$2^{2}\left(a^{2}\right)^{2}-\left(-3a^{4}\right)+\left(-3a^{2}\right)^{2}-20a^{4}$$

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

$$2^{2}a^{4}-\left(-3a^{4}\right)+\left(-3a^{2}\right)^{2}-20a^{4}$$

Calculate 2 to the power of 2 and get 4.

$$4a^{4}-\left(-3a^{4}\right)+\left(-3a^{2}\right)^{2}-20a^{4}$$

The opposite of -3a^{4} is 3a^{4}.

$$4a^{4}+3a^{4}+\left(-3a^{2}\right)^{2}-20a^{4}$$

Combine 4a^{4} and 3a^{4} to get 7a^{4}.

$$7a^{4}+\left(-3a^{2}\right)^{2}-20a^{4}$$

Expand \left(-3a^{2}\right)^{2}.

$$7a^{4}+\left(-3\right)^{2}\left(a^{2}\right)^{2}-20a^{4}$$

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

$$7a^{4}+\left(-3\right)^{2}a^{4}-20a^{4}$$

Calculate -3 to the power of 2 and get 9.

$$7a^{4}+9a^{4}-20a^{4}$$

Combine 7a^{4} and 9a^{4} to get 16a^{4}.

$$16a^{4}-20a^{4}$$

Combine 16a^{4} and -20a^{4} to get -4a^{4}.

$$-4a^{4}$$

Expand

$$-4a^{4}$$

Solution Steps

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

$$2^{2}\left(a^{2}\right)^{2}-\left(-3a^{4}\right)+\left(-3a^{2}\right)^{2}-20a^{4}$$

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

$$2^{2}a^{4}-\left(-3a^{4}\right)+\left(-3a^{2}\right)^{2}-20a^{4}$$

Calculate 2 to the power of 2 and get 4.

$$4a^{4}-\left(-3a^{4}\right)+\left(-3a^{2}\right)^{2}-20a^{4}$$

The opposite of -3a^{4} is 3a^{4}.

$$4a^{4}+3a^{4}+\left(-3a^{2}\right)^{2}-20a^{4}$$

Combine 4a^{4} and 3a^{4} to get 7a^{4}.

$$7a^{4}+\left(-3a^{2}\right)^{2}-20a^{4}$$

Expand \left(-3a^{2}\right)^{2}.

$$7a^{4}+\left(-3\right)^{2}\left(a^{2}\right)^{2}-20a^{4}$$

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

$$7a^{4}+\left(-3\right)^{2}a^{4}-20a^{4}$$

Calculate -3 to the power of 2 and get 9.

$$7a^{4}+9a^{4}-20a^{4}$$

Combine 7a^{4} and 9a^{4} to get 16a^{4}.

$$16a^{4}-20a^{4}$$

Combine 16a^{4} and -20a^{4} to get -4a^{4}.

$$-4a^{4}$$