Solve (s+sqrt{2})(s-sqrt{2})

$$( s + \sqrt { 2 } ) ( s - \sqrt { 2 } )$$

Evaluate

$$s^{2}-2$$

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}.

$$s^{2}-\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$s^{2}-2$$

Differentiate w.r.t. s

$$2s$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(s^{2}-\left(\sqrt{2}\right)^{2})$$

The square of \sqrt{2} is 2.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s^{2}-2)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2s^{2-1}$$

Subtract 1 from 2.

$$2s^{1}$$

For any term t, t^{1}=t.

$$2s$$