Please explain how to solve this:

(�ã5 + 4)(�ã5 - 1)

there's nothing to solve

do you want to multiply

(√5 + 4)(√5 - 1) ?
Just multiply like any binomials:

√5√5 + 4√5 - 1√5 - 4*1
= 5 + 3√5 - 4
= 1 + 3√5

We are to multiply & simplify. My teacher foiled it but I think she made a mistake because the answer she gave was 1+4�ã5 & someone else said the answer should be 3�ã5+1. I'm confused on the foiling.

She foiled it this way:
�ã5*�ã5 -�ã5 + 5*�ã5 - 4 = 5 + 4*�ã5 - 4
= 1+4�ã5

To solve the expression (�ã5 + 4)(�ã5 - 1), we can use the distributive property of multiplication over addition.

First, let's consider the expression inside the parentheses:

�ã5 + 4

This portion can't be simplified further because the terms are not like terms (they cannot be combined).

Similarly, for the expression inside the second parentheses:

�ã5 - 1

Again, we cannot further simplify this because we have a square root.

Now, let's apply the distributive property by multiplying each term in the first parentheses by each term in the second parentheses:

(�ã5 * �ã5) + (�ã5 * -1) + (4 * �ã5) + (4 * -1)

Simplifying these multiplications, we have:

5 + (�ã5 * -1) + (4 * �ã5) + (-4)

Next, let's simplify the two remaining multiplications:

(�ã5 * -1) = -�ã5
(4 * �ã5) = 4�ã5

Now we can substitute these values back into the expression:

5 + (-�ã5) + (4�ã5) + (-4)

Finally, we combine like terms:

5 - 4 + (4�ã5 - �ã5)

Simplifying further:

1 + 3�ã5 - �ã5

And combining the last two terms:

1 + 2�ã5

So, the simplified expression is: 1 + 2�ã5.