Question
Download Solution PDFSimplify,
\(\frac{x^4 - 2x^2 + 1}{x^2 - 2x + 1}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
(a - b)2 = a2 + b2 - 2ab
(a2 - b2) = (a + b) × (a - b)
(a + b)2 = a2 + b2 + 2ab
Calculation:
\(\frac{x^4 - 2x^2 + 1}{x^2 - 2x + 1}\)
⇒ {(x2)2 + 1 - 2 × (x2) × 1}/(x - 1)2
⇒ (x2 - 1)2/(x - 1)2
⇒ {(x + 1)2(x - 1)2}/(x - 1)2
⇒ (x + 1)2 = x2 + 2x + 1
∴ The correct option is 3.
Last updated on Jul 22, 2025
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