Multiply and simplify if possible.
(3−√5)(7−√5)
Show steps
FOIL method:
(3−√5)(7−√5)
= 3(7) + 3(-√5) - √5(7) - √5(-√5)
= 21 - 3√5 - 7√5 + 5
Combine like terms:
= 26 - 10√5
Final answer:
(3−√5)(7−√5) = 26 - 10√5
To multiply (3−√5) and (7−√5), we will use the FOIL method.
FOIL stands for First, Outer, Inner, Last, and it helps us keep track of all the terms we need to multiply together.
First, we multiply the first terms of each binomial:
(3−√5) * 7 = 21−7√5.
Next, we multiply the outer terms of each binomial:
(3−√5) * -√5 = -3√5+5.
Then, we multiply the inner terms of each binomial:
√5 * 7 = 7√5.
Finally, we multiply the last terms of each binomial:
√5 * -√5 = -5.
Now, we can combine the like terms:
(21−7√5) + (-3√5+5) + 7√5 - 5.
Simplifying further, we have:
21 - 5 + 5 + (-7√5 - 3√5 + 7√5).
Combining like terms again, we get:
21 - 5 + 5 - 3√5 + 7√5.
Simplifying this expression, we have:
21 - √5.
So, the simplified form of (3−√5)(7−√5) is 21 - √5.