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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply x^{\frac{1}{2}}-y+1 by x^{\frac{1}{2}}+y-1 and combine like terms.

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

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

$$x^{1}-y^{2}+2y-1$$

Calculate x to the power of 1 and get x.

$$x-y^{2}+2y-1$$

Differentiate w.r.t. x

$$1$$