Solve operatorname{er}(sqrt{2}-3sqrt{5})(sqrt{2}+3sqrt{5})

$$\operatorname { er } ( \sqrt { 2 } - 3 \sqrt { 5 } ) ( \sqrt { 2 } + 3 \sqrt { 5 } )$$

Evaluate

$$-43er$$

Solution Steps

Use the distributive property to multiply er by \sqrt{2}-3\sqrt{5}.

$$\left(er\sqrt{2}-3er\sqrt{5}\right)\left(\sqrt{2}+3\sqrt{5}\right)$$

Apply the distributive property by multiplying each term of er\sqrt{2}-3er\sqrt{5} by each term of \sqrt{2}+3\sqrt{5}.

$$er\left(\sqrt{2}\right)^{2}+3er\sqrt{2}\sqrt{5}-3er\sqrt{5}\sqrt{2}-9er\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{2} is 2.

$$er\times 2+3er\sqrt{2}\sqrt{5}-3er\sqrt{5}\sqrt{2}-9er\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$er\times 2+3er\sqrt{10}-3er\sqrt{5}\sqrt{2}-9er\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$er\times 2+3er\sqrt{10}-3er\sqrt{10}-9er\left(\sqrt{5}\right)^{2}$$

Combine 3er\sqrt{10} and -3er\sqrt{10} to get 0.

$$er\times 2-9er\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$er\times 2-9er\times 5$$

Multiply -9 and 5 to get -45.

$$er\times 2-45er$$

Combine er\times 2 and -45er to get -43er.

$$-43er$$

Differentiate w.r.t. r

$$-43e$$