# 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+16Answer by praseenakos@yahoo.com(507)   (Show Source): You can put this solution on YOUR website!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.