Solve (sqrt{5}-a)*(-a-sqrt{5})

$$( \sqrt { 5 } - a ) \cdot ( - a - \sqrt { 5 } )$$

Evaluate

$$a^{2}-5$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{5}-a by each term of -a-\sqrt{5}.

$$\sqrt{5}\left(-a\right)-\left(\sqrt{5}\right)^{2}-a\left(-a\right)+a\sqrt{5}$$

The square of \sqrt{5} is 5.

$$\sqrt{5}\left(-a\right)-5-a\left(-a\right)+a\sqrt{5}$$

Multiply -1 and -1 to get 1.

$$\sqrt{5}\left(-a\right)-5+aa+a\sqrt{5}$$

Multiply a and a to get a^{2}.

$$\sqrt{5}\left(-a\right)-5+a^{2}+a\sqrt{5}$$

Combine \sqrt{5}\left(-1\right)a and a\sqrt{5} to get 0.

$$-5+a^{2}$$

Differentiate w.r.t. a

$$2a$$

Steps Using Derivative Rule for Sum

Apply the distributive property by multiplying each term of \sqrt{5}-a by each term of -a-\sqrt{5}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\sqrt{5}\left(-a\right)-\left(\sqrt{5}\right)^{2}-a\left(-a\right)+a\sqrt{5})$$

The square of \sqrt{5} is 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\sqrt{5}\left(-a\right)-5-a\left(-a\right)+a\sqrt{5})$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\sqrt{5}\left(-a\right)-5+aa+a\sqrt{5})$$

Multiply a and a to get a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\sqrt{5}\left(-a\right)-5+a^{2}+a\sqrt{5})$$

Combine \sqrt{5}\left(-1\right)a and a\sqrt{5} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-5+a^{2})$$

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}.

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

Subtract 1 from 2.

$$2a^{1}$$

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

$$2a$$