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.
To simplify (25 - √2 + 37 - √3)^2, we first need to expand the expression using the formula (a + b)^2 = a^2 + 2ab + b^2.
So, we have:
(25 - √2 + 37 - √3)^2
= (25 + 37) - 2(25)(√2) - 2(25)(√3) + (√2)^2 + 2(√2)(37) + (√2)(√3) + 37^2 + 2(37)(√3) + (√3)^2
= 62 - 50√2 - 75√3 + 2 + 74√2 + √6 + 1369 + 74√3 + 3
= 1371 - 50√2 - 1√3 + 74√2 + 74√3 + √6
Therefore, the simplified form of (25 - √2 + 37 - √3)^2 is 1371 + 24√2 + 73√3 + √6.