Simplify the expression: ((25)^4 + 1250 + 1 - (25)^2) / ((25)^2 + 25 + 1).

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Accepted Answer

Step 1: Calculate powers of 25.
- (25)^2 = 625
- (25)^4 = (25^2)^2 = 625^2 = 390625

Step 2: Substitute values into numerator:
Numerator = 390625 + 1250 + 1 - 625
= 390625 + 1250 + 1 - 625
= 390625 + 1250 - 624
= 390625 + 626
= 391251

Step 3: Calculate denominator:
Denominator = 625 + 25 + 1 = 651

Step 4: Divide numerator by denominator:
391251 ÷ 651 = 601 (since 651 * 601 = 391251)

Therefore, the simplified value of the expression is 601.

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