1.2 Evaluate
and Simplify Algebraic Expressions
Power
An expression formed
by repeated multiplication of the same factor
Variable
A letter that is used
to represent one or more numbers
Term
In an expression that
can be written as a sum, the parts added together are called terms.
Coefficient
When a term is a
product of a number and a power of a variable, the number is called the
coefficient of the power.
Identity
A statement that
equates two equivalent expressions
|
ORDER OF OPERATIONS |
|
|
Step 1 First, do operations that
occur within _grouping symbols._ |
1 + 72 · (5 - 3) |
|
Step 2 Next, evaluate _powers._ |
= 1 + 72 · 2 |
|
Step
3 Then, do multiplications and divisions from _left
to right_. |
= 1 + 49 ·
2 |
|
Step
4 Finally, do additions and subtractions from _left
to right__. |
= 1 + 98 |
|
|
= 99 |
Example 1
Evaluate -6y2 - 11y + 34 when y
= -5.
Solution
-6y2
-
11 + 34
=
-6(_-5_)2 -
11(_-5_) + 34 Substitute -5
for y.
=
-6(_25_)
-
11(_-5_) + 34 Evaluate the power.
=
_-150_
+ _55_ + 34 Multiply.
=
-61 Add.
TERMS AND COEFFICIENTS
In an expression that
can be written as a sum, the parts added together are called _terms_.
A term that has a variable part is a _variable
term_.
A term that has no
variable part is a _constant term_.
When a term is a product of a number and a power
of a variable, the number is called the _coefficient_ of the power.
Example 2
Simplify by combining like terms
a.
11x
- 5x
b.
2(y
+ 5) - 3(y
- 9)
c.
14x
- 6y
+ 5x + 13y
Solution
|
a. 11x - 5x =
(_11 - 5_)x |
Distributive property |
|
= _6x_ |
Add coefficients |
|
b.
2(y + 5) -
3(y - 9) |
|
|
= 2y + 10 -
3y + 27 |
Distributive property |
|
|
|
|
= (_2y -
3y_) +
(_10 + 27_) |
Group like terms. |
|
|
|
|
= _-
y_ + _37_ |
Combine like terms. |
|
|
|
|
c.
14x -
6y + 5x + 13y |
|
|
= (_14x +
5x_) + (_-6y+ 13y_) |
Group like terms. |
|
|
|
|
= _19x _+
_7
y |
Combine like terms. |
|
|