Solve {left(2x^3-5/3right)}^3

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

Evaluate

$$\frac{\left(6x^{3}-5\right)^{3}}{27}$$

Solution Steps

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

$$8\left(x^{3}\right)^{3}-20\left(x^{3}\right)^{2}+\frac{50}{3}x^{3}-\frac{125}{27}$$

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

$$8x^{9}-20\left(x^{3}\right)^{2}+\frac{50}{3}x^{3}-\frac{125}{27}$$

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

$$8x^{9}-20x^{6}+\frac{50}{3}x^{3}-\frac{125}{27}$$

Expand

$$8x^{9}-20x^{6}+\frac{50x^{3}}{3}-\frac{125}{27}$$

Solution Steps

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

$$8\left(x^{3}\right)^{3}-20\left(x^{3}\right)^{2}+\frac{50}{3}x^{3}-\frac{125}{27}$$

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

$$8x^{9}-20\left(x^{3}\right)^{2}+\frac{50}{3}x^{3}-\frac{125}{27}$$

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

$$8x^{9}-20x^{6}+\frac{50}{3}x^{3}-\frac{125}{27}$$