Solve [(2x-a)(a-x)^2]^frac{1{3}}

$$[ ( 2 x - a ) ( a - x ) ^ { 2 } ] ^ { \frac { 1 } { 3 } }$$

Evaluate

$$\sqrt[3]{2x-a}\left(a-x\right)^{\frac{2}{3}}$$

Solution Steps

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

$$\left(\left(2x-a\right)\left(a^{2}-2ax+x^{2}\right)\right)^{\frac{1}{3}}$$

Use the distributive property to multiply 2x-a by a^{2}-2ax+x^{2} and combine like terms.

$$\left(4xa^{2}-5x^{2}a+2x^{3}-a^{3}\right)^{\frac{1}{3}}$$

Factor

$$\sqrt[3]{2x-a}\left(a-x\right)^{\frac{2}{3}}$$