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# Find the GCD of the following

x^{2} + 3xy + 2y^{2}, x^{2} + 5xy + 6y^{2}

Answer :

Given,

X^{2} + 3xy + 2y^{2} = x^{2} + xy + 2xy + 2y^{2}

= x(x + y) + 2y(x + y)

= (x + 2y)(x + y)

x^{2} + 5xy + 6y^{2} = x^{2} + 3xy + 2xy + 6y^{2}

= x(x + 3y) + 2y(x + 3y)

= (x + 2y)(x + 3y)

Greatest common divisor = (x + 2y)

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