To simplify (25–√+37–√)^2, we first expand the expression using the distributive property of exponents.
(25–√+37–√)^2 = (25–√+37–√)(25–√+37–√)
Next, we multiply each term in the first parentheses by each term in the second parentheses using the distributive property.
(25–√)(25–√) + (25–√)(37–√) + (37–√)(25–√) + (37–√)(37–√)
Now, we simplify each product by multiplying the terms.
(625 - 50√ + √^2) + (925 - 25√ + 37√ - √^2) + (925 - 25√ + 37√ - √^2) + (1369 - 74√ + √^2)
Simplifying further, we get
625 - 50√ + 25 + 925 - 25√ + 37√ - 37 + 925 - 25√ + 37√ - 25 + 1369 - 74√ + 37
Combine like terms:
(625 + 25 + 925 - 37 + 925 - 25 - 25 + 1369) + (-50√ - 25√ + 37√ - 25√ - 74√)
Now, simplify:
(2941) + (-63√)
Therefore, the simplified form of (25–√+37–√)^2 is 2941 - 63√.
Simplify (25–√+37–√)^2 . Show your work. Justify each step.
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