Solve (8)a^{3}*(-b^3)^2+(-2ab^2)^3

$$( 8 ) a ^ { 3 } \cdot ( - b ^ { 3 } ) ^ { 2 } + ( - 2 a b ^ { 2 } ) ^ { 3 }$$

Evaluate

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Solution Steps

Calculate -b^{3} to the power of 2 and get \left(b^{3}\right)^{2}.

$$8a^{3}\left(b^{3}\right)^{2}+\left(-2ab^{2}\right)^{3}$$

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

$$8a^{3}\left(b^{3}\right)^{2}+\left(-2\right)^{3}a^{3}\left(b^{2}\right)^{3}$$

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

$$8a^{3}\left(b^{3}\right)^{2}+\left(-2\right)^{3}a^{3}b^{6}$$

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

$$8a^{3}\left(b^{3}\right)^{2}-8a^{3}b^{6}$$

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

$$8a^{3}b^{6}-8a^{3}b^{6}$$

Combine 8a^{3}b^{6} and -8a^{3}b^{6} to get 0.

$$0$$

Factor

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Solution Steps

Factor out 8.

$$8\left(a^{3}b^{6}-\left(ab^{2}\right)^{3}\right)$$

Simplify.

$$0$$