SOLUTION: Find the LCM of q^2-4 and q^2+10q+16

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Question 81306: Find the LCM of q^2-4 and q^2+10q+16
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
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QUESTION:

Find the LCM of q^2-4 and q^2+10q+16


ANSWER:

Using the identity, (a+b)(a-b)= a^2 -b^2

q^2 - 4 = q^2 - 2^2 can be factorised as (q+2)(q-2).

Using the method of splitting the middle term q^2+10q+16 can be factorised as follows.....


q^2 + 10q + 16 = q^2 + 8q + 2q +16


==> = (q^2 + 8q) + (2q +16)


Now take out the common terms.....



==> = q(q + 8) + 2(q +8)


Here (q+8) is common to both the terms.....so we can write it as...



==> = (q+2)(q + 8)


So the expressions have become


q^2 - 4 = (q+2)(q-2).
q^2 + 10q + 16= (q+2)(q + 8)






So the LCM of the given expressions is (q+2)(q-2)(q+8)
That is take all the factors of both the expressions excluding the repeated one.


Hope you found the explanation useful.

Regards.

Praseena.