Solve a^2+1/2ab+(-1/2ab)+1/2b^2+(-1/4ab)+(-frac{1}{2}b^2)

$$a ^ { 2 } + \frac { 1 } { 2 } a b + ( - \frac { 1 } { 2 } a b ) + \frac { 1 } { 2 } b ^ { 2 } + ( - \frac { 1 } { 4 } a b ) + ( - \frac { 1 } { 2 } b ^ { 2 } )$$

Evaluate

$$-\frac{ab}{4}+a^{2}$$

Solution Steps

Combine \frac{1}{2}ab and -\frac{1}{2}ab to get 0.

$$a^{2}+\frac{1}{2}b^{2}-\frac{1}{4}ab-\frac{1}{2}b^{2}$$

Combine \frac{1}{2}b^{2} and -\frac{1}{2}b^{2} to get 0.

$$a^{2}-\frac{1}{4}ab$$

Factor

$$\frac{a\left(4a-b\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{4a^{2}+2ab-2ab+2b^{2}-ab-2b^{2}}{4}$$

Consider 4a^{2}+2ab-2ab+2b^{2}-ab-2b^{2}. Multiply and combine like terms.

$$4a^{2}-ab$$

Consider 4a^{2}-ab. Factor out a.

$$a\left(4a-b\right)$$

Rewrite the complete factored expression.

$$\frac{a\left(4a-b\right)}{4}$$