How does the FOIL method work for multiplying and simplifying (3 - √5)(7 - √5)?
FOIL stands for First, Outer, Inner, Last. It is a method used to multiply two binomials.
To use the FOIL method to multiply and simplify (3 - √5)(7 - √5), follow these steps:
- First: Multiply the first terms of each binomial. In this case, it's 3 × 7 = 21.
- Outer: Multiply the outer terms of each binomial. In this case, it's 3 × -√5 = -3√5.
- Inner: Multiply the inner terms of each binomial. In this case, it's -√5 × 7 = -7√5.
- Last: Multiply the last terms of each binomial. In this case, it's -√5 × -√5 = 5.
Now add all the products you got from the FOIL method:
21 - 3√5 - 7√5 + 5
Simplify by combining like terms:
26 - 10√5
So, (3 - √5)(7 - √5) = 26 - 10√5.