Solve 1/5a^{2}-1/2ab)^{2}+1/2ab*(a^2-1/2ab)-frac{3}{5}a^2*(-a)^2-frac{3}{10}a*(a^2b)

$$\frac { 1 } { 5 } a ^ { 2 } - \frac { 1 } { 2 } a b ) ^ { 2 } + \frac { 1 } { 2 } a b \cdot ( a ^ { 2 } - \frac { 1 } { 2 } a b ) - \frac { 3 } { 5 } a ^ { 2 } \cdot ( - a ) ^ { 2 } - \frac { 3 } { 10 } a \cdot ( a ^ { 2 } b )$$

Factor

$$\frac{a\left(2a-5b\right)}{10}$$

Solution Steps

Factor out \frac{1}{10}.

$$\frac{2a^{2}-5ab}{10}$$

Consider 2a^{2}-5ab. Factor out a.

$$a\left(2a-5b\right)$$

Rewrite the complete factored expression.

$$\frac{a\left(2a-5b\right)}{10}$$

Evaluate

$$-\frac{ab}{2}+\frac{a^{2}}{5}$$