Factorize: x4 + x2y2 + y4 - Vidyadip

Question

Factorize:
x⁴ + x²y² + y⁴

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Answer

x⁴ + x²y² + y⁴
Adding x²y² and subtracting x²y² to the given equation
= x⁴ + x²y² + y⁴ + x²y² - x²y²
= x⁴ + 2x²y²+ y⁴ - x²y²
= (x²)² + 2 × x² × y² + (y²)² - (xy)²
Using the identity (p + q)² = p² + q² + 2pq
= (x² + y²)² - (xy)²
Using the identity p² - q² = (p + q)(p - q)
= (x² + y² + xy)(x² + y² - xy)
$\therefore$ x⁴ + x²y² + y⁴ = (x² + y²+ xy)(x² + y² - xy)

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