Let’s find the L.C.M. of the following algebraic expressions:
x2-y2 + z2-2xz, x2-y2-z2 + 2yz, xy + zx + y2-z2
Factors of x2-y2 + z2-2xz
= x2 + z2-2xz-y2
=(x-z)2-y2
=(x-z + y)(x-z-y)
Factors of x2-y2-z2 + 2yz
= x2-(y2 + z2-2yz)
= x2-(y-z)2
=(x + y-z)(x-y + z)
Factors of xy + zx + y2-z2
=x(y + z) + (y + z)(y-z)
=(x + y-z)(y + z)
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-y2 + z2-2xz, x2-y2-z2 + 2yz, xy + zx + y2-z2 Is
(x-z + y)(x-z-y)(x-y + z)(y + z)
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