Simplify (25–√+37–√)2 . Show your work. Justify each step.

Answer 1

To simplify (25–√+37–√)2, we first need to expand the expression by using the distributive property:

(25–√+37–√)2 = (25–√)² + 2(25–√)(37–√) + (37–√)²

Next, we use the FOIL method to expand each of the terms in the expression:

(25–√)² = 25² - 2(25)(√) + (√)² = 625 - 50√ + √²
(25–√)(37–√) = (25)(37) - (25)(√) - (37)(√) + √² = 925 - 62√ + √²
(37–√)² = 37² - 2(37)(√) + (√)² = 1369 - 74√ + √²

Now, we combine the like terms:
625 - 50√ + √² + 2(925 - 62√ + √²) + 1369 - 74√ + √²
= 625 - 50√ + √² + 1850 - 124√ + 2√² + 1369 - 74√ + √²
= 3844 - 248√ + 4√²

Therefore, (25–√+37–√)2 simplifies to 3844 - 248√ + 4√².