(A) + (B),and then simplifying as much as possible. Subtracting B from A means setting up the difference as
(A) − (B),and then simplifying as much as possible.
(4 x y + 7) + (8 y + 9 x y)and setting up the difference A − B gives:
(4 x y + 7) − (8 y + 9 x y)
(A) + (B) always simplifies directly to A + B. The brackets can just be dropped. |
(A) − (B) simplifies to A − B except in these two cases: Exception # 1: If B is a negative monomial then the subtraction of a negative must be replaced by an addition. Exception # 2: If B is a multinomial then the − sign of the subtraction must be distributed over each term of the multinomial. The result, as explained below, is that each term of B has its sign reversed when the brackets are dropped. |
a − (b − c) ← start with this a − (b + (− c) ) change subtraction into addition of a negative a + (− 1) · (b + (− c) ) change the other subtraction into multiplication by − 1 a + (− 1) · b + (− 1) · (− c) use the distributive law to distribute the − 1 a − b + (− 1) · (− c) change multiplication by − 1 back to subtraction a − b + c a negative times a negative gives a positive
Recall that like terms are terms in an expression that differ only in their coefficients; they have identical variable factors. Like terms can be added or subtracted by adding or subtracting their coefficients (essentially by factoring with the distributive law). |
use the commutative law to sort the terms use the distributive law to combine (factor) the two like terms simplify
Algebra Coach Exercises |