Download simplifying expressions

Simplifying Expressions
Objectives:
…to simplify an expression by performing the distributive property
…to simplify an expression by combining like terms
Assessment Anchor:
Not Available At This Time
Vocabulary alert!!
DISTRIBUTIVE PROPERTY – a way to simplify an
expression that is multiplying a
single term by a group of terms
NOTES and EXAMPLES
The distributive property is a very important property in mathematics, which
allows us to simplify expressions in the following manner:
***For any numbers a, b and c…
a(b + c) = ab + ac
Look at the following examples that show the distributive property being applied:
Ex. #1:
3(5 + 4) = 3(5) + 3(4)
3(9) = 15 + 12
27 = 27
Ex. #2:
8(2 + 6) = 8(2) + 8(6)
8(8) = 16 + 48
64 = 64
Ex. #3:
5 • 4 + 5 • 9 = 5(4 + 9)
20 + 45 = 5(13)
65
= 65
Ex. #4:
7 • 3 + 7 • 8 = 7(3 + 8)
21 + 56 = 7(11)
77
= 77
“Notice that whether the property is applied either
forward or backward... the distributive property
maintains the value of the expression.”
Simplifying Expressions
“Take what’s outside the parenthesis, and multiply it
by each of the things inside the parenthesis.”
Ex. #5:
5(x + 3) = 5(x) + 5(3)
= 5x + 15
Ex. #6:
2(3x – 4) = 2(3x) – 2(4)
= 6x – 8
7)
4(x + 6) =
9)
6(3x – 4) =
8)
-2(x + 3) =
10)
-8(2k + 1) =
-------------------------------------------------------------------------------------------------11) -2(2x – 7) =
13) -3(9 – 2y) =
12)
-7(5x – 2) =
14)
-4(-3 – 5k) =
Vocabulary alert!!
TERM – a number, a variable, or product of a number and
a variable(s)
CONSTANT – a term with no variable part (i.e. a number)
COEFFICIENT – a number that multiplies a variable
LIKE TERMS – terms that have the same variable part
Simplifying Expressions
Combining like terms is another very important idea in mathematics, and is
accomplished by adding the coefficients of the like terms. This is possible because
of the distributive property.
***For any numbers a and b…
Ex. #15:
ax + bx = (a+b)x
4x + 7x = (4 + 7)x
= 11x
Ex. #16)
10y – 4y = (10 – 4)y
= 6y
Vocabulary familiarization activity
8x + 9 – 3 + 7y + 4x – 3y + 11 – xy
Terms?
Coefficients?
Constants?
Like terms?
17)
8y – 6y =
20)
10x + 5x =
18)
8x + 2y + 4x + 7y =
21)
-3x + 10x + 4 – 18 =
19)
9 + 4x + 3y + 8y =
22)
4 – 12x + 4x – 10 =
--------------------------------------------------------------------------------------------------23)
5 + x – 6y + x – 3y =
25)
-4 – 2x – 9y + 3 – 7x + 2y =
24)
-3xy + 4x – 9x + 4xy – 12x =
26)
8xy + 8x – 10 – 7y =
--------------------------------------------------------------------------------------------------27)
2(x + 7) + 9x – 3 =
28)
-3(2x + 9) + 2(5x + 1) =