Transcript 1.1 Real Numbers & Number Operations 8/26/11

Daily Homework Quiz
Warm Up
1. Evaluate 3( x + 2 ) – 8x when x = 3.
ANSWER
–9
2. Evaluate 5p 2 – (6p – 4) when p = – 4.
ANSWER
108
Evaluate the expression.
3. ( – 5 )2
ANSWER
25
4. 32 ÷ 8 • (– 2 + 5 )2
ANSWER
36
1.3 Simplifying Algebraic
Expressions
8/27/12
Vocabulary
Terms :
The parts of the expression that are
separated by + or – sign.
Coefficient :
When a term is the product of a number and
a power of a variable, the number is the
coefficient.
Ex. 2x or 2x3 2 is the coefficient
If the variable doesn’t have a number in
front of it, the coefficient is 1.
Ex. x, x2 both have a coefficient of 1.
Like terms :
Terms that have the same variable parts
Constant term :
A term that consists of just a number.
Ex: 5x + 8
Example 1
Identify Terms in an Expression
Identify the terms in the expression – 11 – 7x – 2x 2 .
Terms : The parts of the expression that are
separated by + or – sign.
ANSWER
Terms:
– 11, – 7x, and – 2x 2
Example 2
Identify Coefficients and Like Terms
Identify the coefficients and like terms in the
expression x 2 – 7x + 5 – 3x 2 – 10 .
ANSWER
Coefficients:1, -7, and -3.
Like terms: x 2 and -3x 2
: 5 and -10
More Examples
1. Identify the terms, coefficients, and like terms in the
expression 4x 3 – 5x 2 + x 2 – 9x – 9x 3 + 7x.
ANSWER
terms: 4x 3, – 5x 2, x 2, – 9x, – 9x 3, 7x;
coefficients: 4, – 5, 1, – 9, – 9, 7;
like terms: 4x 3 and – 9x 3,– 5x 2 and x 2, – 9x and 7x
Example 3
Simplify by Combining Like Terms
Simplify the expression.
a. 5x + 9x
This step is optional
SOLUTION
a. 5x + 9x = (5+9)x
= 14x
Example 3
Simplify by Combining Like Terms
Simplify the expression.
b. 2x2 + 3x – x2 + 6x
Parenthesis is optional
= ( 2x2 – x2) + (3x + 6x)
Group like
terms.
= x2 + 9x
Important Note: When moving terms around, make sure
you keep the sign that’s in front of it.
Example 3
Simplify by Combining Like Terms
c. 4y – 7x – 12y + 3x
= ( 4y – 12y) + (– 7x + 3x) Group like
terms.
= – 8y – 4x
Distributive Prop: In general:
a(b+c) = ab + ac
multiply
multiply
Example 4
Simplify Expressions with Grouping Symbols
Simplify the expression.
a. 12 – 5 ( x – 1)
SOLUTION
a. 12 – 5(x – 1) = 12 – 5x + 5
= – 5x + (12 + 5)
= – 5x + 17
Distribute -5
Group like terms.
CLT.
Example 4
Simplify Expressions with Grouping Symbols
b. 4 ( 6 – x) + 3 ( x – 8)
= 24 – 4x + 3x – 24
Distributive
property
= (– 4x + 3x) + ( 24 – 24) Group like
terms.
= –x
Checkpoint
Simplify Expressions
Simplify the expression.
2. 7x – 3x
ANSWER
4x
3. 1 + x + 10x – 8
ANSWER
11x – 7
4. x + x2 – 4x2 – 5x
ANSWER
–3x2 – 4x
5. 3 + 2 ( x + 4 )
ANSWER
2x + 11
6. x – 6 ( x – 2)
ANSWER
–5x + 12
Homework
WS 1.3 Practice A