Solve (x^3-1)^3=

$$( x ^ { 3 } - 1 ) ^ { 3 } =$$

Evaluate

$$\left(x^{3}-1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{3}-1\right)^{3}.

$$\left(x^{3}\right)^{3}-3\left(x^{3}\right)^{2}+3x^{3}-1$$

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

$$x^{9}-3\left(x^{3}\right)^{2}+3x^{3}-1$$

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

$$x^{9}-3x^{6}+3x^{3}-1$$

Expand

$$x^{9}-3x^{6}+3x^{3}-1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{3}-1\right)^{3}.

$$\left(x^{3}\right)^{3}-3\left(x^{3}\right)^{2}+3x^{3}-1$$

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

$$x^{9}-3\left(x^{3}\right)^{2}+3x^{3}-1$$

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

$$x^{9}-3x^{6}+3x^{3}-1$$