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

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

Evaluate

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

Solution Steps

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

$$x^{3}\left(4\left(x^{2}\right)^{2}-12x^{2}+9\right)$$

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

$$x^{3}\left(4x^{4}-12x^{2}+9\right)$$

Use the distributive property to multiply x^{3} by 4x^{4}-12x^{2}+9.

$$4x^{7}-12x^{5}+9x^{3}$$

Expand

$$4x^{7}-12x^{5}+9x^{3}$$

Solution Steps

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

$$x^{3}\left(4\left(x^{2}\right)^{2}-12x^{2}+9\right)$$

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

$$x^{3}\left(4x^{4}-12x^{2}+9\right)$$

Use the distributive property to multiply x^{3} by 4x^{4}-12x^{2}+9.

$$4x^{7}-12x^{5}+9x^{3}$$