Question 81306
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.