Combine Like Terms and Distributive Property In this lesson you will be shown how to combine like terms along with using the distributive property Terms in an algebraic expression are separated by addition or subtraction signs ID: 188986
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Slide1
Combine Like Terms and Distributive PropertySlide2
Combine Like Terms and Distributive Property
In this lesson, you will be shown how to combine like terms along with using the distributive property.Slide3
Terms
in an algebraic expression are separated by addition or subtraction signs.
How many terms are in this expression?
Like terms are terms that look alike.
So, what are like terms?Slide4
More specifically, Like Terms are terms that have the same variable raised to the same power (exponent).
Now, let’s give this a try.Slide5
Combine like terms.
Identify like terms
.
Combine coefficients: 14 – 5 = 9
A.
14
a
– 5
a
9
a
B.
7
y
+ 8 – 3
y
– 1 +
y
Identify like terms ; the coefficient of y is 1, because 1y = y.
5
y
+ 7
Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7Slide6
Combine like terms.
Identify like terms
; the coefficient of q is 1, because 1q = q.
Combine coefficients: 4 – 1 = 3
Identify like terms;
the coefficient of c is 1, because 1c = c.
6
3
q
C.
4
q
–
q
D.
5
c
+ 8
– 4
c
– 2 –
c
Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6Slide7
E. 4
m
+ 9
n
– 2
4m
+ 9n – 2
Combine like terms.
No like terms
.
F. 5
m
*
7
m
– 8 + 4
35
m
– 4 Slide8
Remember, to
simplify
an expression means to perform all possible operations, including combining like terms.
In other words, simplify means solve!Slide9
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)Slide10
Distribute
A. 6(x - 3)
B.
2(y
+ 1)C. 3(a
- 1)
6x - 18
2y + 2
3a – 3Slide11
Now we will use the distributive property first, then combine like terms second.Slide12
1. Simplify 6(5 +
n
)
– 2
n.
Distributive Property
.
Multiply.
6(5 +
n
) – 2n
30 + 6
n
– 2
n
6
(5)
+
6
(
n) – 2n
30 + 4n
Combine coefficients 6
– 2 = 4.Slide13
2. Simplify 3(
c +
7)
–
c.
Distributive Property
.
Multiply.
3(
c
+ 7) – c
3
c
+ 21
–
c
3
(
c
)
+ 3(7) –
c2c + 21
Combine coefficients 3
– 1 = 2.Slide14
3. 4(3x + 6)
7x
4. 6(x + 5) + 3x
Simplify.Slide15
4. 5(2x - 3)
+
4x
10x – 15 + 4x
14x - 15