Solve f(x)=(x^3-3x)^2

$$f ( x ) = ( x ^ { 3 } - 3 x ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$\left(x^{3}\right)^{2}-6x^{3}x+9x^{2}$$

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

$$x^{6}-6x^{3}x+9x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{6}-6x^{4}+9x^{2}$$

Expand

$$x^{6}-6x^{4}+9x^{2}$$

Solution Steps

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

$$\left(x^{3}\right)^{2}-6x^{3}x+9x^{2}$$

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

$$x^{6}-6x^{3}x+9x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{6}-6x^{4}+9x^{2}$$