Solve (-3a)^2-a^4+(-2a^2)^3

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

Evaluate

$$a^{2}\left(9-a^{2}-8a^{4}\right)$$

Solution Steps

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

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

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

$$9a^{2}-a^{4}+\left(-2a^{2}\right)^{3}$$

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

$$9a^{2}-a^{4}+\left(-2\right)^{3}\left(a^{2}\right)^{3}$$

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

$$9a^{2}-a^{4}+\left(-2\right)^{3}a^{6}$$

Calculate -2 to the power of 3 and get -8.

$$9a^{2}-a^{4}-8a^{6}$$

Expand

$$9a^{2}-a^{4}-8a^{6}$$

Solution Steps

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

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

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

$$9a^{2}-a^{4}+\left(-2a^{2}\right)^{3}$$

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

$$9a^{2}-a^{4}+\left(-2\right)^{3}\left(a^{2}\right)^{3}$$

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

$$9a^{2}-a^{4}+\left(-2\right)^{3}a^{6}$$

Calculate -2 to the power of 3 and get -8.

$$9a^{2}-a^{4}-8a^{6}$$