Q4 K of 42 Page 136

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

3a2-5ab-12b2, a5-27a2b3, 9a2 + 24ab + 16b2


factors of 3a2-5ab-12b2

=3a2-9ab + 4ab-12b2


=3a(a-3b) + 4b(a-3b)


=(3a + 4b)(a-3b)


Factors of a5-27a2b3


=a2(a3-27b3)


=a2(a-3b)(a2 + 3ab + 9b2)


Factors of 9a2 + 24ab + 16b2


=9a2 + 12ab + 12ab + 16b2


=3a(3a + 4b) + 4b(3a + 4b)


=(3a + 4b)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 3a2-5ab-12b2, a5-27a2b3, 9a2 + 24ab + 16b2is


a2(a-3b)(a2 + 3ab + 9b2) (3a + 4b)2


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