Q. 4 H4.4( 9 Votes )
Let’s find the L.C.M. of the following algebraic expressions:
x2-xy-2y2, 2x2-5xy + 2y2, 2x2 + xy-y2
Answer :
Factors of x2-xy-2y2
= x2-2xy + xy-2y2
=x(x-2y) + y(x-2y)
=(x + y)(x-2y)
Factors of 2x2-5xy + 2y2
=2x2-4xy-xy + 2y2
=2x(x-2y)-y(x-2y)
=(2x-y)(x-2y)
Factors of 2x2 + xy-y2
=2x2 + 2xy-xy-y2
=2x(x + y)-y(x + y)
=(2x-y) (x + y)
LCM is the lowest common multiple, which is the product of all the common factors taken once and the remaining factors as it is.
∴ the LCM of x2-xy-2y2, 2x2-5xy + 2y2, 2x2 + xy-y2 is
(x + y)(x-2y) (2x-y)
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