When calculating with letters it’s important to know what “like terms” are.
Like terms are terms that have the same letters (and those letters have the same powers)
E.g. 3a and 8a and 333a are like terms. But 12a and 4ab and 9c and 12a2 are not like terms.
When adding with letters you can only add like terms. In equations with letters we usually try and simplify the equation as must as possible.
Calculation with letters is not so different than calculating with numbers. See here:
4+4+4 = 3*4
a+a+a = 3*a (but we don’t write the multiplication sign between the number and the letters) so
a+a+a = 3a
Following this:
3*4 + 3*4 + 4 = 4+4+4 + 4+4+4 + 4 =7*4
3a + 3a + a = a+a+a + a+a+a + a = 7a
And that also means:
3*4 + 3*4 + 4 + 6 = 4+4+4 + 4+4+4 + 4 + 6 = 7*4 + 6 (we can’t write the 6 with the 4’s)
3a + 3a + a + v = a+a+a + a+a+a + a + v = 7a + v (we can’t write the v with de a’s)
E.g.
Simplify 6p + 7c +c2 + 33p
Solution:
6p + 7c + c2 + 33p =
39p + 7c + c2
We can’t simplify it any further. Some students find this difficult because you don’t get a real answer in the form of a number. But without more information this is as far as you can get.
These rules also apply to substraction with letters.
These are the first steps in algebra.