Solve 9*left(sqrt{5}+2right)left(sqrt{5}-2right)

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

Evaluate

$$9$$

Solution Steps

Use the distributive property to multiply 9 by \sqrt{5}+2.

$$\left(9\sqrt{5}+18\right)\left(\sqrt{5}-2\right)$$

Apply the distributive property by multiplying each term of 9\sqrt{5}+18 by each term of \sqrt{5}-2.

$$9\left(\sqrt{5}\right)^{2}-18\sqrt{5}+18\sqrt{5}-36$$

The square of \sqrt{5} is 5.

$$9\times 5-18\sqrt{5}+18\sqrt{5}-36$$

Multiply 9 and 5 to get 45.

$$45-18\sqrt{5}+18\sqrt{5}-36$$

Combine -18\sqrt{5} and 18\sqrt{5} to get 0.

$$45-36$$

Subtract 36 from 45 to get 9.

$$9$$

Factor

$$3^{2}$$