find G.C.D of the following algebraic expression: $x^{3} - 3 x^{2} y, x^{2} - 9 y^{2}$

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Solution

$x^{3} - 3 x^{2} y = x^{2} (x - 3 y)$ $∴$ Factors of $x^{3} - 3 x^{2} y = x^{2} (x - 3 y)$ $x^{2} - 9 y^{2} = (x + 3 y) (x - 3 y)$ $∴$ Factors of $x^{2} - 9 y^{2} = (x + 3 y) (x - 3 y)$ GCD is the greatest common divisor, which is equal to the product of all the common divisors. $∴$ the GCD of $x^{3} - 3 x^{2} y, x^{2} - 9 y^{2}$ is $(x - 3 y)$

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