# Simplifying Algebraic Expressions combining like terms Math 1

Simplifying Algebraic Expressions (combining like terms) Math 1

Combining like terms with addition � RULE: add the coefficients of the like terms and keep the same variables with the coefficient Expression: 7 a + 2 b + a + 3 b Variable coefficient The first step is to identify like terms. This is easy to do if you focus on the variable parts of each term. In other words, ignore the coefficients and see which variables are identical. Then, combine the coefficients to combine like terms.

Now actually combine the like terms 7 a + 2 b + a + 3 b 7 a + 2 b + 3 b ( we are using the commutative property to rearrange so the like terms are grouped together) 8 a + 5 b So our “new” expression is: 8 a + 5 b

Example: 2 b + 9 a + 5 ab+ 3 b 2 b+3 b + 9 a + 5 ab 5 b + 9 a + 5 ab Notice that the only set of like terms were 2 b and 3 b. Just because 9 a and 5 ab have “a” they are NOT alike so we don’t combine them.

Example: 5 a + b + 7 + 3 b + 10 a + 1 5 a + 10 a + b + 3 b + 7 + 1 (7 and 1 are called CONSTANTS. Just because they don’t have a variable, they ARE called like terms as well because there is more then one constant. ) 15 a + 4 b + 8

Combining like terms with substraction � RULE: � Move like terms together keeping the plus or minus sign that is in front of the term; and � Combine like terms by adding or subtracting their coefficients. � Notice the one big difference in the second step! You are allowed to rearrange the terms as long as you keep the signs in front of them! Expression: 7 a - 2 b - a + 3 b Variable coefficient The first step is to identify like terms. This is easy to do if you focus on the variable parts of each term. In other words, ignore the coefficients and see which variables are identical. Then, combine the coefficients to combine like terms.

Now actually combine the like terms 7 a - 2 b - a + 3 b 7 a - a + 3 b-2 b ( we are using the commutative property to rearrange so the like terms are grouped together) 6 a + b So our “new” expression is: 6 a + b

Example: 3 b - 9 a - 5 ab - 2 b 3 b – 2 b - 9 a - 5 ab Notice that the only set of like terms were 3 b and -2 b. Just because -9 a and -5 ab have “a” they are NOT alike so we don’t combine them.

Example: 5 a - b + 7 + 3 b + 10 a - 1 5 a + 10 a + 3 b - b + 7 - 1 (7 and 1 are called CONSTANTS. Just because they don’t have a variable, they ARE called like terms as well because there is more then one constant. ) 15 a + 2 b + 6

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