Solve y=(2x^3-5)^3

$$y = ( 2 x ^ { 3 } - 5 ) ^ { 3 }$$

Solve for y

$$y=\left(2x^{3}-5\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x^{3}-5\right)^{3}.

$$y=8\left(x^{3}\right)^{3}-60\left(x^{3}\right)^{2}+150x^{3}-125$$

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

$$y=8x^{9}-60\left(x^{3}\right)^{2}+150x^{3}-125$$

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

$$y=8x^{9}-60x^{6}+150x^{3}-125$$

Solve for x

$$x=\frac{2^{\frac{2}{3}}\sqrt[3]{\sqrt[3]{y}+5}}{2}$$