How to Simplify Expressions without Parentheses



Vocabulary:


Variable- a letter representing an unknown value; the value changes or varies depending on the situation, thus called a variable


Coefficient– a number in front of the variable; for example 5x; 5 is the coefficient


Constant– the part of the expression or rule that does not change; n + 6 or y + 3; 6 and 3 are the constants


Terms– each addend in the above expressions are called a terms


Like terms– have the same variable parts and exponents


Example:3x+5+ 3y +4x+12


The like terms are 3x and 4x ; 5 and 12

Thus, the expression becomes 7x + 3y + 12.

Note, it is customary to write the terms in alphabetical order, and write the constants last.


Some students would say 3x and 3y are considered like terms. This assumption is incorrect. Why? The variables are different.


Steps:


1. Change all subtraction to addition of the opposite of the following term. In other words, change the subtraction operand (-) to addition (+) and change the sign of the following number. If the number is positive, change it to a negative number and vice versa.

2. Combine like variables. Since, we changed everything to addition in the first step, add. Just remember the rules to adding integers.


Simplify the following expressions:


1) -8k + 2k

2) 11c + c + 5c

3) 5x + y – 6x + y

4) 12a – 16b – 8ab +16b

5) 9x – 4y – 3x + 6y






Answers:


1) -8k + 2k (Add coefficients of like terms)

-6k


2) 11c + c + 5c (Add coefficients of like terms)

17c (Note: “1” is the coefficient for c; the original problem could be rewritten as 11c + 1c + 5c)


3) 5x + y – 6x + y (Change subtraction to addition)

5x + 1y + (-6x) +1y (Add coefficients of like terms)

-x + 2y


4) 12a – 16b – 8ab +16b (Change subtraction to addition)

12a + (-16b) + (-8ab) + 16b (Add coefficients of like terms)

12a - 8ab


5) 9x – 4y – 3x + 6y (Change subtraction to addition)

9x + (-4y) + (-3x) + 6y (Add coefficients of like terms)

6x + 2y



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