Doug C. answered • 12/04/24
Math Tutor with Reputation to make difficult concepts understandable
This algebraic expression contains 4 terms, The + sign in from of each term travels with the term. You can visualize additional + signs separating each term:
(+8c) + (+5) + (+3) + (+4c)
If the expression was instead: 8c - 5 + 3 - 4c you would visualize:
(+8c) + (-5) + (+3) + (-4c)
By commutative property for addition:
8c + 4c + 5 + 3
The +5 and +3 are constant terms (no variable). The +8c and + 4c are similar terms.
+8c and + 4c combine to +12c (adding their respective numerical coefficients). You can visualize why by using the distributive property: 8c + 4c = c(8+4) = c(12) = 12c.
The constant terms combine to +8. So the simplified algebraic expression is:
12c + 8 (which you could also write as: 8 + 12c)
Understanding how to simplify the above expression is key to being able to solve equations.
Example:
8c + 5 + 3 + 4c = -3c - 7 +5
12c + 8 = -3c - 2
12c + 3c = -2 - 8
15c = -10
c = -10/15 = -2/3
