Solve 3(-2a^{3})^3-2(2a^3)^2+5(-3a^3)

$$3 ( - 2 a ^ { 3 } ) ^ { 3 } - 2 ( 2 a ^ { 3 } ) ^ { 2 } + 5 ( - 3 a ^ { 3 } )$$

Evaluate

$$-24a^{9}-8a^{6}-15a^{3}$$

Solution Steps

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

$$3\left(-2\right)^{3}\left(a^{3}\right)^{3}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3\left(-2\right)^{3}a^{9}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

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

$$3\left(-8\right)a^{9}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

Multiply 3 and -8 to get -24.

$$-24a^{9}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

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

$$-24a^{9}-2\times 2^{2}\left(a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

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

$$-24a^{9}-2\times 2^{2}a^{6}+5\left(-3\right)a^{3}$$

Calculate 2 to the power of 2 and get 4.

$$-24a^{9}-2\times 4a^{6}+5\left(-3\right)a^{3}$$

Multiply 2 and 4 to get 8.

$$-24a^{9}-8a^{6}+5\left(-3\right)a^{3}$$

Multiply 5 and -3 to get -15.

$$-24a^{9}-8a^{6}-15a^{3}$$

Expand

$$-24a^{9}-8a^{6}-15a^{3}$$

Solution Steps

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

$$3\left(-2\right)^{3}\left(a^{3}\right)^{3}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3\left(-2\right)^{3}a^{9}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

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

$$3\left(-8\right)a^{9}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

Multiply 3 and -8 to get -24.

$$-24a^{9}-2\times \left(2a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

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

$$-24a^{9}-2\times 2^{2}\left(a^{3}\right)^{2}+5\left(-3\right)a^{3}$$

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

$$-24a^{9}-2\times 2^{2}a^{6}+5\left(-3\right)a^{3}$$

Calculate 2 to the power of 2 and get 4.

$$-24a^{9}-2\times 4a^{6}+5\left(-3\right)a^{3}$$

Multiply 2 and 4 to get 8.

$$-24a^{9}-8a^{6}+5\left(-3\right)a^{3}$$

Multiply 5 and -3 to get -15.

$$-24a^{9}-8a^{6}-15a^{3}$$