X2 - xy - 2y2= x2 - (2 - 1) xy - 2y2= x2 - 2xy + xy - 2y2= X(x - 2y) + y(x - 2y)= (x - 2y) (x + y) ....(1)And, 2x2 - xy - Y2= 2x2 - (2 - 1)xy - y2= 2x2 - 2xy + xy - y2= 2x ( x - y) + y(x - y) = (2x + y) (x - y) ....(2)from EQUATION (1) & (2) H.C.F of given polynomial = 1

"> X2 - xy - 2y2= x2 - (2 - 1) xy - 2y2= x2 - 2xy + xy - 2y2= X(x - 2y) + y(x - 2y)= (x - 2y) (x + y) ....(1)And, 2x2 - xy - Y2= 2x2 - (2 - 1)xy - y2= 2x2 - 2xy + xy - y2= 2x ( x - y) + y(x - y) = (2x + y) (x - y) ....(2)from EQUATION (1) & (2) H.C.F of given polynomial = 1

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The H. C. F. of x2 - xy - 2y2 and 2x2 - xy - y2 is:

General Knowledge General Awareness in General Knowledge 11 months ago

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Calculation:Given polynomial,X2 - xy - 2y2= x2 - (2 - 1) xy - 2y2= x2 - 2xy + xy - 2y2= X(x - 2y) + y(x - 2y)= (x - 2y) (x + y) ....(1)And, 2x2 - xy - Y2= 2x2 - (2 - 1)xy - y2= 2x2 - 2xy + xy - y2= 2x ( x - y) + y(x - y) = (2x + y) (x - y) ....(2)from EQUATION (1) & (2) H.C.F of given polynomial = 1

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