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Multiple Choice Questions

The HCF of x4 ndash y4 and x6 ndash y6 is ........

Quantitative Aptitude (CDS) LCM, HCF

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The HCF of (x⁴ – y⁴) and (x⁶ – y⁶) is

x² – y²

x – y

x³ – y³

x⁴ – y⁴

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Explanation:

Let f1 (x) = (x⁴ – y⁴) = [((x²)² – (y²)²]
= (x²– y²) (x² + y²)
= (x – y) (x + y) (x² +y²)
And f2 (x) = (x⁶– y⁶)
= (x³ )² – (y³)² = (x³ + y³) (x³ – y³)
= (x + y) (x² – xy + y²) (x-y) x² + xy + y²)
= (x-y) (x+y) (x² – xy + y²) (x² + xy + y²)
HCF of [f1 (x), f2 (x)] = (x – y) (x + y) = x² – y²