1. Algebra 1 Glencoe McGraw-Hill JoAnn Evans
Math 8H
The Distributive Property
And
Combining Like Terms
(Day 2)
Algebra Glencoe McGraw-Hill JoAnn Evans

2. Remember --
Like terms are terms that have the same variables raised to the same powers.
In a term that is the product of a number and a variable, the number is the coefficient of the variable.
Like terms can be combined by adding or subtracting their coefficients.

3. = -x + -2y + -z Add the opposite first.
Terms are separated by addition signs. To determine the terms of a variable expression, you must first change all subtractions to “add the opposite”.
4x2 + 3x Three terms: 4x2, 3x, and 9
-x – 2y – z
= -x + -2y + -z Add the opposite first.
Three terms: -x, -2y, and –z
-y – 3r
= -y + -3r Two terms: -y and -3r

4. Simplify by using the distributive property and then combining like terms. Next, evaluate by substituting in the given value for the variable.
19 – 4x(y – 6) + 5y when y = 2 and x = 3
= x(y + -6) + 5y
= xy + 24x + 5y
= (3)(2) + 24(3) + 5(2) =
= 77

5. 3x(x – 9) + 4(y + 7) when x = 2 and y = -3 = 3x(x + -9) + 4(y + 7)
Simplify by using the distributive property and then combining like terms. Next, evaluate by substituting in the given value for the variable.
3x(x – 9) + 4(y + 7) when x = 2 and y = -3
= 3x(x + -9) + 4(y + 7)
= 3x x + 4y + 28
= 3(2) (2) + 4(-3)
= 3(4) (-12) + 28 = =
= -26

6. Remember about negatives that appear in front of parentheses!!
There is an “invisible 1” outside the parentheses.
x - (2x + 3)
= x – 1(2x + 3) It’s there. Really!
= x + -1(2x + 3) Add the opposite.
= x + -2x Distribute.
= -1x Combine like terms.
= -x – Simplify.

7. Distributing a Fraction:
To multiply by ⅛,
divide by 8.
⅛(16x + 40)
= ⅛(16x) + ⅛(40)
= 2x + 5
-¼(12y2 – 16)
= -¼(12y )
= -¼(12y2) + ( -¼)(-16)
= -3y2 + 4
To multiply by – ¼ ,
divide by -4.

8. How can you tell if a variable expression is simplified?
It must pass three tests:
1. There are no more parentheses or other grouping symbols left in the expression.
2. There are no like terms that haven’t been combined.
3. There are no “double signs”.