Factorise : \(x^4 + x^2y^2 + y^2\).

1.	Factorise : \(x^4 + x^2y^2 + y^2\).
Answer» \(x^4 + x^2y^2 + y^4\) = x⁴ + 2x²y² + y⁴ - x²y²(Note : Add and subtract x²y²) = (x² + y²)² - x²y² = (x² + y²)² - (xy)² = (x² + y² + xy)(x² + y² -xy).

Answer»

\(x^4 + x^2y^2 + y^4\) = x⁴ + 2x²y² + y⁴ - x²y²(Note : Add and subtract x²y²)

= (x² + y²)² - x²y²

= (x² + y²)² - (xy)²

= (x² + y² + xy)(x² + y² -xy).

Discussion