Solve left(x^3-6xright)^3

$${ \left( { x }^{ 3 } -6x \right) }^{ 3 }$$

Evaluate

$$\left(x\left(x^{2}-6\right)\right)^{3}$$

Solution Steps

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

$$\left(x^{3}\right)^{3}-18\left(x^{3}\right)^{2}x+108x^{3}x^{2}-216x^{3}$$

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

$$x^{9}-18\left(x^{3}\right)^{2}x+108x^{3}x^{2}-216x^{3}$$

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

$$x^{9}-18x^{6}x+108x^{3}x^{2}-216x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$x^{9}-18x^{7}+108x^{3}x^{2}-216x^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$x^{9}-18x^{7}+108x^{5}-216x^{3}$$

Expand

$$x^{9}-18x^{7}+108x^{5}-216x^{3}$$

Solution Steps

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

$$\left(x^{3}\right)^{3}-18\left(x^{3}\right)^{2}x+108x^{3}x^{2}-216x^{3}$$

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

$$x^{9}-18\left(x^{3}\right)^{2}x+108x^{3}x^{2}-216x^{3}$$

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

$$x^{9}-18x^{6}x+108x^{3}x^{2}-216x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$x^{9}-18x^{7}+108x^{3}x^{2}-216x^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$x^{9}-18x^{7}+108x^{5}-216x^{3}$$