Q. 4 D4.6( 11 Votes )
Let’s find the L.C.M. of the following algebraic expressions:
ab4-8ab, a2b4 + 8a2b, ab4-4ab2
Answer :
factors of ab4-8ab
=ab(b3-8)
=ab(b-2)(b2 + 2b + 4)
Factors of a2b4 + 8a2b
=a2b(b3 + 8)
= a2b(b + 2)( b2-2b + 4)
Factors of ab4-4ab2
=ab2(b2-4)
= ab2(b + 2)(b-2)
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 ab4-8ab, a2b4 + 8a2b, ab4-4ab2 is
a2b2(b + 2)(b-2)(b2-2b + 4)(b2 + 2b + 4)
= a2b2(b3 + 8) (b3-8)
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