Solve y=x^frac{2{3}}(x-2)^2

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

Solve for y

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

Solution Steps

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

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

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

$$y=x^{\frac{2}{3}}x^{2}-4x^{\frac{2}{3}}x+4x^{\frac{2}{3}}$$

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and 2 to get \frac{8}{3}.

$$y=x^{\frac{8}{3}}-4x^{\frac{2}{3}}x+4x^{\frac{2}{3}}$$

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and 1 to get \frac{5}{3}.

$$y=x^{\frac{8}{3}}-4x^{\frac{5}{3}}+4x^{\frac{2}{3}}$$