Solve (x^4-x)^3

$$( x ^ { 4 } - x ) ^ { 3 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{4}-x\right)^{3}.

$$\left(x^{4}\right)^{3}-3\left(x^{4}\right)^{2}x+3x^{4}x^{2}-x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$x^{12}-3\left(x^{4}\right)^{2}x+3x^{4}x^{2}-x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{12}-3x^{8}x+3x^{4}x^{2}-x^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$x^{12}-3x^{9}+3x^{4}x^{2}-x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$x^{12}-3x^{9}+3x^{6}-x^{3}$$

Expand

$$x^{12}-3x^{9}+3x^{6}-x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{4}-x\right)^{3}.

$$\left(x^{4}\right)^{3}-3\left(x^{4}\right)^{2}x+3x^{4}x^{2}-x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$x^{12}-3\left(x^{4}\right)^{2}x+3x^{4}x^{2}-x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{12}-3x^{8}x+3x^{4}x^{2}-x^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$x^{12}-3x^{9}+3x^{4}x^{2}-x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$x^{12}-3x^{9}+3x^{6}-x^{3}$$