# How would you simplify (sqrt 5+4)(sqrt 5-1)?

##### 2 Answers
Apr 27, 2018

$1 + 3 \sqrt{5}$

#### Explanation:

$\text{note that } \sqrt{a} \times \sqrt{a} = a$

$\text{expand the factors using FOIL}$

$= 5 - \sqrt{5} + 4 \sqrt{5} - 4$

$= 1 + 3 \sqrt{5}$

Apr 27, 2018

$1 + 3 \sqrt{5}$

#### Explanation:

To simplify this, we need to use the distributive property of multiplication. We can use the FOIL method, which means to multiply the first numbers, then the outer numbers, then the inner numbers, and finally the last numbers of each binomial:

$\sqrt{5} \cdot \sqrt{5} = 5$ | $4 \cdot \sqrt{5} = 4 \sqrt{5}$
$\sqrt{5} \cdot - 1 = - \sqrt{5}$ | $4 \cdot - 1 = - 4$

Finally, we add the like terms together to simplify the expression:

$5 - 4 + 4 \sqrt{5} - \sqrt{5}$
$1 + 3 \sqrt{5}$