(a-1)x^2+a^2xy+(a+1)y^2

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

Taking (a-1)x outside
and y ouside

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

Taking {x+(a+1)y} outside

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

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Similar questions

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

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

a x + b (sec ({tan}^{- 1} x)) = c

a y + b (sec ({tan}^{- 1} y)) = c

The product of all the factors of determinant

$∣ ∣ ∣ ∣ ∣ \begin{matrix} x & y & 1 x^{2} & y^{2} & 1 x^{3} & y^{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ is:

^{Solve for x and y}

^{ax + by = 2ab}

bx + ay = a²+ b²

\frac{1}{x} + \frac{1}{y} = 2

\frac{1}{x} + \frac{1}{y} = \frac{1}{2}

\frac{1}{x} + \frac{1}{y} = \frac{2}{a}

\frac{1}{x} + \frac{1}{y} = \frac{2}{b}

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