# Combining Like Terms Distributive Property by pptfiles

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```									    Warm Up
Simplify.

1.     9 + 13 - 5 + 3 20
2.     16 - 8 + 4 - 1 11
3.     6 + 9 - 10 + 3 8
4.     17 + 8 - 20 - 2 3

Course 3
Homework Answers
1)    20
2)    5
3)    4
15) ½ cup
4)    3
16) 2 cups
5)    8      17) 3 cups
6)    23.2   18) 4 ½ cups
7)    80     19) \$6.20
8)    52
9)    25
10)   6
11)   42
12)   135
13)   77
14)   72
Combining Like Terms
Distributive Property

7/17/2013
Terms in an expression are separated by
plus or minus signs.

Like terms can be grouped together
because they have the same variable raised
to the same power.

Helpful Hint
Constants such as 4, 0.75, and 11 same
Equivalent expressions have the are like
terms because none the variables.
value for all values ofof them have a variable.
Combine like terms.

A. 14a – 5a               Identify like terms.
9a                     Combine coefficients: 14 – 5 = 9

Identify like terms ; the
B. 7y + 8 – 3y – 1 + y
coefficient of y is 1, because
1y = y.

5y + 7                 Combine coefficients: 7 – 3 + 1 = 5
and 8 – 1 = 7
Combine like terms.
Identify like terms; the
coefficient of q is 1, because
C. 4q – q
1q = q.
3q                      Combine coefficients: 4 – 1 = 3

D. 5c + 8 – 4c – 2 – c     Identify like terms; the
coefficient of c is 1, because
1c = c.

6                     Combine coefficients: 5 – 4 – 1 = 0
and 8 – 2 = 6
Combine like terms.

E. 4m + 9n – 2

4m + 9n – 2         No like terms.
When a variable expression has ( ) and
we cannot combine what is inside them,
we will need to distribute any
multiplication attached outside. We will
use the distributive property to help.

Here’s how:     a (b + c) = ab + ac.

For example, 2 (x + 4) = 2x + 2(4) .

Remember to combine any like terms
after using the distributive property.
To simplify an expression, perform all
possible operations, including
combining like terms.

Remember!
The Distributive Property states that a(b + c)
= ab + ac for all real numbers a, b, and c. For
example, 2(3 + 5) = 2(3) + 2(5).
Simplify 6(5 + n) – 2n.

6(5 + n) – 2n
6(5) + 6(n) – 2n     Distributive Property.
30 + 6n – 2n         Multiply.
30 + 4n              Combine coefficients 6 – 2 = 4.
Simplify 3(c + 7) – c.

3(c + 7) – c
3(c) + 3(7) – c          Distributive Property.
3c + 21 – c              Multiply.
2c + 21                  Combine coefficients 3 – 1 = 2.
Simplify

4(3x + 6) - 7x

6(x + 5) + 3x
Sometimes using the distributive property will require distributing
negative values, or even negative signs resulting from subtractions
being changed to additions. Be sure that you continue to change all
subtractions to additions 1st, even if this means attaching a
negative sign to ( ).
1) 2x - 3(x + 4)

2) 7y - (y + 4)

3) -8r - 2(r - 5)
4) 7(4p - 3) - 7(2p + 3)

5) -2(5x - 3) - 3( x + 2)

6) -5(x + 4) - (3x - 2)

7) - (x + 5) - 2(4x - 7)
n   Class activity – with a buddy complete
puzzle worksheet

Homework – WS 2.2

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