Solve y=(x^2-1)^3

$$y = ( x ^ { 2 } - 1 ) ^ { 3 }$$

Solve for y

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

Solution Steps

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

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

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

$$y=x^{6}-3\left(x^{2}\right)^{2}+3x^{2}-1$$

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

$$y=x^{6}-3x^{4}+3x^{2}-1$$

Solve for x

$$x=\sqrt{\sqrt[3]{y}+1}$$

$$x=-\sqrt{\sqrt[3]{y}+1}\text{, }y\geq -1$$