Solve 2/2(a/2)^3/2-2m(a/2)^2

$$\frac { 2 } { 2 } ( \frac { a } { 2 } ) ^ { 3 / 2 } - 2 m ( \frac { a } { 2 } ) ^ { 2 }$$

Factor

$$\frac{a^{\frac{3}{2}}\left(-2\sqrt{a}m+\sqrt{2}\right)}{4}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\frac{\sqrt{2}a^{\frac{3}{2}}}{2}-ma^{2}}{2}$$

Consider \sqrt{\frac{1}{2}}a^{\frac{3}{2}}-ma^{2}. Factor out a^{\frac{3}{2}}.

$$a^{\frac{3}{2}}\left(\frac{\sqrt{2}}{2}-m\sqrt{a}\right)$$

Rewrite the complete factored expression.

$$\frac{a^{\frac{3}{2}}\left(\frac{\sqrt{2}}{2}-m\sqrt{a}\right)}{2}$$

Evaluate

$$\frac{a^{\frac{3}{2}}\left(-2\sqrt{a}m+\sqrt{2}\right)}{4}$$