Q2 of 227 Page 89

Find the GCD of the following

x2 + 3xy + 2y2, x2 + 5xy + 6y2

Given,


X2 + 3xy + 2y2 = x2 + xy + 2xy + 2y2


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


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


x2 + 5xy + 6y2 = x2 + 3xy + 2xy + 6y2


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


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


Greatest common divisor = (x + 2y)


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