Solve (2x^3-6)^3

$$( 2 x ^ { 3 } - 6 ) ^ { 3 }$$

Evaluate

$$8\left(x^{3}-3\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x^{3}-6\right)^{3}.

$$8\left(x^{3}\right)^{3}-72\left(x^{3}\right)^{2}+216x^{3}-216$$

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

$$8x^{9}-72\left(x^{3}\right)^{2}+216x^{3}-216$$

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

$$8x^{9}-72x^{6}+216x^{3}-216$$

Expand

$$8x^{9}-72x^{6}+216x^{3}-216$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x^{3}-6\right)^{3}.

$$8\left(x^{3}\right)^{3}-72\left(x^{3}\right)^{2}+216x^{3}-216$$

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

$$8x^{9}-72\left(x^{3}\right)^{2}+216x^{3}-216$$

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

$$8x^{9}-72x^{6}+216x^{3}-216$$