Question
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.
Answer
To simplify (25–√ + 37–√)², we need to first expand the expression using the distributive property.
(25–√ + 37–√)² = (25–√ + 37–√)(25–√ + 37–√)
Using the distributive property, we can expand this expression:
= 25(25) - 25(√) - √(25) + √(√) + 37(25) - 37(√) - √(37) + √(√)
= 625 - 25√ - 5√ + √² + 925 - 37√ - 7√ + √²
Now, simplify the expression by combining like terms:
= 625 + 925 - 25√ - 5√ - 37√ - 7√ + √² + √²
= 1550 - 69√ + 2
So, (25–√ + 37–√)² simplifies to 1550 - 69√ + 2.