Solve b^frac{1{2}}(b^frac{1{2}}-b^frac{5{2}})

$$b ^ { \frac { 1 } { 2 } } ( b ^ { \frac { 1 } { 2 } } - b ^ { \frac { 5 } { 2 } } )$$

Evaluate

$$b-b^{3}$$

Solution Steps

Use the distributive property to multiply b^{\frac{1}{2}} by b^{\frac{1}{2}}-b^{\frac{5}{2}}.

$$\left(b^{\frac{1}{2}}\right)^{2}-b^{\frac{1}{2}}b^{\frac{5}{2}}$$

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

$$b^{1}-b^{\frac{1}{2}}b^{\frac{5}{2}}$$

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

$$b^{1}-b^{3}$$

Calculate b to the power of 1 and get b.

$$b-b^{3}$$

Factor

$$b\left(-b-1\right)\left(b-1\right)$$