Find the coefficient of x2 expansion of

Find the coefficient of x² expansion of (x² + x + 1)² + (x² – x + 1)²

Answer :

Given:

The expression, (x² + x + 1)² + (x² – x + 1)²

(x² + x + 1)² + (x² – x + 1)² = [((x² + 1) + x)² + [(x² + 1) – x)²]
= (x² + 1)² + x² + 2 (x² + 1) (x) + (x² + 1)² + x² – 2 (x² + 1) (x)

= (x²)² + (1)² + 2 × x² × 1 + x² + (x²)² + 1 + 2 × x² + 1 + x²

= x⁴ + 1 + 2x² + x² + x⁴ + 1 + 2x² + x²

= 2x⁴ + 6x² + 2

∴ Co-efficient of x² is 6.

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