Solve (sqrt{2}-a)(sqrt{2}+a)=

$$( \sqrt { 2 } - a ) ( \sqrt { 2 } + a ) =$$

Evaluate

$$2-a^{2}$$

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}.

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

The square of \sqrt{2} is 2.

$$2-a^{2}$$

Differentiate w.r.t. a

$$-2a$$

Steps Using Derivative Rule for Sum

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

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

The square of \sqrt{2} is 2.

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

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}.

$$2\left(-1\right)a^{2-1}$$

Multiply 2 times -1.

$$-2a^{2-1}$$

Subtract 1 from 2.

$$-2a^{1}$$

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

$$-2a$$