Solve (7x^frac{1{3}}-3x^frac{2{3}})^2

$$( 7 x ^ { \frac { 1 } { 3 } } - 3 x ^ { \frac { 2 } { 3 } } ) ^ { 2 }$$

Evaluate

$$x^{\frac{2}{3}}\left(-3\sqrt[3]{x}+7\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7x^{\frac{1}{3}}-3x^{\frac{2}{3}}\right)^{2}.

$$49\left(x^{\frac{1}{3}}\right)^{2}-42x^{\frac{1}{3}}x^{\frac{2}{3}}+9\left(x^{\frac{2}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$49x^{\frac{2}{3}}-42x^{\frac{1}{3}}x^{\frac{2}{3}}+9\left(x^{\frac{2}{3}}\right)^{2}$$

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

$$49x^{\frac{2}{3}}-42x^{1}+9\left(x^{\frac{2}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 2 to get \frac{4}{3}.

$$49x^{\frac{2}{3}}-42x^{1}+9x^{\frac{4}{3}}$$

Calculate x to the power of 1 and get x.

$$49x^{\frac{2}{3}}-42x+9x^{\frac{4}{3}}$$

Expand

$$9x^{\frac{4}{3}}-42x+49x^{\frac{2}{3}}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7x^{\frac{1}{3}}-3x^{\frac{2}{3}}\right)^{2}.

$$49\left(x^{\frac{1}{3}}\right)^{2}-42x^{\frac{1}{3}}x^{\frac{2}{3}}+9\left(x^{\frac{2}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$49x^{\frac{2}{3}}-42x^{\frac{1}{3}}x^{\frac{2}{3}}+9\left(x^{\frac{2}{3}}\right)^{2}$$

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

$$49x^{\frac{2}{3}}-42x^{1}+9\left(x^{\frac{2}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 2 to get \frac{4}{3}.

$$49x^{\frac{2}{3}}-42x^{1}+9x^{\frac{4}{3}}$$

Calculate x to the power of 1 and get x.

$$49x^{\frac{2}{3}}-42x+9x^{\frac{4}{3}}$$