(a-1)x2+a2xy+(a+1)y2

ans (x+ay+y)(ax-x+y)

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Solution

(a - 1)x² + a²xy + (a + 1)y²

= (a - 1)x² + (a² - 1 + 1)xy + (a + 1)y²

= (a - 1)x² + {(a - 1)(a + 1) + 1}xy + (a + 1)y²

= (a - 1)x² + (a - 1)(a + 1)xy + xy + (a + 1)y²

= (a - 1)x{x + (a + 1)y} + y{x + (a + 1)y}

= (x + ay + y)(ax - x + y)

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