Solve (x^frac{1{2}}+y^frac{1{2}})(x^frac{1{2}}-y^frac{1{2}})

$$( x ^ { \frac { 1 } { 2 } } + y ^ { \frac { 1 } { 2 } } ) ( x ^ { \frac { 1 } { 2 } } - y ^ { \frac { 1 } { 2 } } )$$

Evaluate

$$x-y$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(x^{\frac{1}{2}}\right)^{2}-\left(y^{\frac{1}{2}}\right)^{2}$$

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

$$x^{1}-\left(y^{\frac{1}{2}}\right)^{2}$$

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

$$x^{1}-y^{1}$$

Calculate x to the power of 1 and get x.

$$x-y^{1}$$

Calculate y to the power of 1 and get y.

$$x-y$$

Differentiate w.r.t. x

$$1$$