Let’s find the L.C.M. of the following algebraic expressions:

x²-xy-2y², 2x²-5xy + 2y², 2x² + xy-y²

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)