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).