1. Algebra 1 Glencoe McGraw-Hill JoAnn Evans
The Distributive Property
And
Combining Like Terms
Algebra Glencoe McGraw-Hill JoAnn Evans

2. Negative factors and subtractions cause some students to make errors when they use the distributive property.
To avoid this pitfall, we’re going to change all subtractions to addition of a negative before performing the distributive property.
-5(x - 2)
Change the subtraction to
addition of a negative.
-5(x +-2)
Perform the distributive
property.
-5x + 10

3. -3(y - 5) -3(y +-5) -3y + 15 -5y(y + 7) (x – 2)(-4x) -5y2 +-35y
Change the subtraction to
addition of a negative.
-3(y +-5)
2. Perform the distributive property.
-3y + 15
Eliminate the double sign in the final answer.
-5y(y + 7)
(x – 2)(-4x)
-5y2 +-35y
(x +-2)(-4x)
Because the -4 is in parentheses, it must be distributed.
-5y2 – 35y
-4x2 + 8x

4. 4u(x – 7) 3z(-5z + 1) 4u(x +-7) -15z2 + 3z 4ux + -28u 4ux - 28u
Eliminate the double sign in the final answer.
4u(x – 7)
3z(-5z + 1)
4u(x +-7)
-15z2 + 3z
4ux + -28u
4ux - 28u
9n(2m – 3)
-(x – 8)
Put variables in alphabetical order.
9n(2m +-3)
-1(x +-8)
18nm + -27n
-1x + 8
18mn – 27n
-x + 8

5. the same variables raised to the same powers.
A term is a number, a variable, or a product or quotient of numbers and variables.
Like terms are terms that contain the same variables, with corresponding variables having the same power.
In other words,
like terms have
the same variables raised to the same powers.

6. Examples of LIKE terms:
7x and x
3xy and xy
2x2 and x2
-6bc and bc
Each pair has the same variables raised to the same power.
Examples of UNLIKE terms:
x and x2
mn and m2n
3xy and 12xyz
The terms are not identical in power and in variables.

7. A negative coefficient is a coefficient of negative one.
In a term that’s the product of a number and a variable, the number is the coefficient of the variable.
12x is the coefficient of x.
-3y is the coefficient of y.
5mn is the coefficient of mn.
What’s the coefficient of this term?
-x2
-1 is the coefficient of x2.
A negative coefficient
is a coefficient of negative one.

8. Like terms can be combined by adding or subtracting the coefficients of the terms.
2(x + 6) – 3
2(x + 6) + -3 2x
2x + 9
3(2x – 8) + 20x
3(2x + -8) + 20x
6x x
26x - 24
16 – (5x + 3)
(5x + 3)
x + -3
– 5x + 13
13 + 8y – 7 – 12y
13 + 8y y
-4y + 6

9. Like terms can be combined by adding or subtracting the coefficients of the terms.
w + 14w – 6w
1w + 14w + -6w 9w
12b2 + 9b2 – 22b2
12b2 + 9b b2
-1b2
-b2
3a2 + 6a + 4a2
7a2 + 6a
4(6p + 7q – 2p)
4(6p + 7q + -2p)
4(4p + 7q)
16p + 28q

10. How can you tell if a variable expression is simplified?
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”.

11. Simplify more complicated expressions:
11 – 2x(z + 3) + 4x – 2 + xz
Change all subtractions to addition of a negative.
x(z + 3) + 4x xz
Perform the distributive property.
xz + -6x + 4x xz
Simplify the expression by combining like terms.
-2x
+ -xz
+ 9
-2x – xz + 9
Eliminate double signs.

12. Simplify more complicated expressions:
x(y + 4) + 15 – 6xy
Change all subtractions to addition of a negative.
x(y + 4) xy
Perform the distributive property.
xy + 4x xy
Simplify the expression by combining like terms. 4x
+ -5xy
+ 15
4x – 5xy + 15
Eliminate double signs.