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