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Question
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
(x2y + xy2), (x2 + xy)
Solution
p(x) = x2y + xy2 = xy(x + y)
g(x) = x2 + xy = x(x + y)
G.C.D = x(x+y)
L.C.M = xy (x +y).
L.C.M × G.C.D = xy(x + y) × x(x + y)
= x2y(x + y)2 …..(1)
p(x) × g(x) = xy(x + y) × x(x + y)
= x2y(x + y)2
From (1) and (2) we get
L.C.M × G.C.D. = p(x) × g(x)
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