Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify (25–√+37–√)2
. Show your work. Justify each step.
(2 points)
To simplify (25-√ + 37-√ )^2, we first expand the expression using FOIL (First, Outer, Inner, Last):
(25-√ + 37-√ )^2 = (25 - √)(25 - √) + (25 - √)(37 - √) + (37 - √)(25 - √) + (37 - √)(37 - √)
Next, we can simplify each multiplication step:
= 625 - 50√ + √^2 + 925 - 62√ + 925 - 62√ + √^2
= 625 - 50√ + 25 + 925 - 62√ + 925 - 62√ + 37
= 1575 - 174√ + 62
= 1637 - 174√
Therefore, the simplified form of (25-√ + 37-√ )^2 is 1637 - 174√.