Q. 4 J4.0( 8 Votes )

# Let’s find the L.C.M. of the following algebraic expressions:(a2 + 2a)2 , 2a3 + 3a2-2a, 2a4-3a3-12a2

factors of (a2 + 2a)2

= a4 + 4a2 + 4a3

= a2(a2 + 4 + 4a)

= a2(a2 + 2a + 2a + 4)

= a2(a(a + 2) + 2(a + 2))

= a2(a + 2)(a + 2)

= a2(a + 2)2

Factors of 2a3 + 3a2-2a

=a(2a2 + 3a-2)

=a(2a2 + 4a-a-2)

=a{2a(a + 2)-1(a + 2)}

=a(a + 2) (2a-1)

Factors of 2a4-3a3-14a2

=a2(2a2-3a-14)

=a2(2a2 + 4a-7a-14)

= a2(2a(a + 2)-7(a + 2))

= a2(2a-7) (a + 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 (a2 + 2a)2, 2a3 + 3a2-2a, 2a4-3a3-12a2 is a2(a + 2)2(2a-1)(2a-7).

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