Q. 4 F4.4( 7 Votes )

# Let’s find the L.C.M. of the following algebraic expressions:p2 + 2p, 2p4 + 3p3-2p2, 2p3-3p2-14p

Factors of p2 + 2p

=p(p + 2)

Factors of 2p4 + 3p3-2p2

=p2(2p2 + 3p-2)

= p2(2p2 + 4p-p-2)

=p2{2p(p + 2)-1(p + 2)}

=p2{(2p-1)(p + 2)}

Factors of 2p3-3p2-14p

=p(2p2-3p-14)

=p(2p2-7p + 4p-14)

=p{p(2p-7) + 2(2p-7)}

=p(p + 2)(2p-7)

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 p2 + 2p, 2p4 + 3p3-2p2, 2p3-3p2-14p is

p2(2p-1)(p + 2) (2p-7)

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