Solve (a+b)^2/2-(a-b)^2/2

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

Evaluate

$$2ab$$

Short Solution Steps

Since \frac{\left(a+b\right)^{2}}{2} and \frac{\left(a-b\right)^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(a+b\right)^{2}-\left(a-b\right)^{2}}{2}$$

Do the multiplications in \left(a+b\right)^{2}-\left(a-b\right)^{2}.

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

Combine like terms in a^{2}+2ab+b^{2}-a^{2}+2ab-b^{2}.

$$\frac{4ab}{2}$$

Divide 4ab by 2 to get 2ab.

$$2ab$$

Expand

$$2ab$$

Short Solution Steps

Since \frac{\left(a+b\right)^{2}}{2} and \frac{\left(a-b\right)^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(a+b\right)^{2}-\left(a-b\right)^{2}}{2}$$

Do the multiplications in \left(a+b\right)^{2}-\left(a-b\right)^{2}.

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

Combine like terms in a^{2}+2ab+b^{2}-a^{2}+2ab-b^{2}.

$$\frac{4ab}{2}$$

Divide 4ab by 2 to get 2ab.

$$2ab$$