Combine%20Like%20Terms%20and%20Distributive%20Property

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Combine Like Terms and Distributive Property

• Dr. Livingston
• CHMS Team 6B

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Combine Like Terms and Distributive Property

• In this lesson, you will be shown how to combine
  like terms along with using the distributive
  property.

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Terms in an algebraic expression are separated by
addition or subtraction signs.
How many terms are in this expression?
So, what are like terms?
Like terms are terms that look alike.
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More specifically, Like Terms are terms that have
the same variable raised to the same power
(exponent).
Now, lets give this a try.
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Combine like terms.
A. 14a 5a
Identify like terms.
9a
Combine coefficients 14 5 9
Identify like terms the coefficient of y is 1,
because 1y y.
B. 7y 8 3y 1 y
5y 7
Combine coefficients 7 3 1 5 and 8 1 7
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Combine like terms.
Identify like terms the coefficient of q is 1,
because 1q q.
C. 4q q
3q
Combine coefficients 4 1 3
Identify like terms the coefficient of c is 1,
because 1c c.
D. 5c 8 4c 2 c
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Combine coefficients 5 4 1 0 and 8 2 6
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Combine like terms.
E. 4m 9n 2
4m 9n 2
No like terms.
F. 5m 7m 8 4
-2m 4
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Remember, to simplify an expression means to
perform all possible operations, including
combining like terms.
In other words, simplify means solve!
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The Distributive Property is an algebra property
which is used to multiply a single term and two
or more terms inside a set of parentheses.
For any numbers a, b, and c,
a(b c)
a(b) a(c)
and
a(b c)
a(b) a(c)
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Distribute

• A. 6(x - 3)
• B. -2(y 1)
• C. -3(a - 1)

6x - 18
-2y (-2)
-3a (-3)
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Now we will use the distributive property first,
then combine like terms second.
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1. 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.
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2. 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.
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Simplify.
3. 4(3x 6) ? 7x
4. 6(x 5) 3x
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4. 5(2x - 3) 4x 10x 15 4x 14x - 15