algebraic equations and expressions

   
combine like terms   
Combine Like Terms
6.) 3x - 6y + 5x - 5y  
7.) 9x² + 8x - 6x + 4x²  
8.) xy² + x²y - 3x²y - xy  
9.) 4(x² - 3x) - 2(x - 2) - (3 - x - x²)
distribute   
IV. Vocabulary: distribute
Simplify by order of operations and the distributive property
2(4 + 5) = 2 · 4 + 2 · 5
2(4)+2(5)= 8 + 10
8 + 10 = 18
  18 = 18
14.) Distribute     3( 4 + 5 - 6 - 3)
 
15.) Distribute     3(x + 4)
 
16.) Distribute by factoring     3x + 12
 
evaluate expression   
2. Evaluate when x = -1 and y = -2:
a.) 5 - x²
b.) - x²
c.) (-x)²
Evaluate the expression when x = - 3 and y = 2.
10.)     x² - y
 
11.)     4x - y
 
12.)     4x - 3y
 
13.)     xy - (x + y)
 
II. Evaluate when x is -1 and y = 4
4.) 2x² + xy  
5.) , read as "x to the y"   Answer
polynomial computation   
I. Vocabulary: evaluate    expression
like terms    combine like terms   
I. Simplify and check answer before completing the next section.
1.] 3(x - 5) - 2(x + 3 - 2y)
2.] -52 - 4(x - y) + 40 - 04
3.] 5x(x2 + 4x - 3) - (x3 - 4x2 - 4)
4.] {3(6 - 7)3 - 22(3 - ( 5 - 1)) }
II. Solve
5.] 3(x - 5) - 2(x + 3 - 2y) = -52 - 4(x - y) + 40 - 04
6.] 5x(x2 + 4x - 3) - (x3 - 4x2 - 4) = {3(6 - 7)3 - 22(3 - ( 5 - 1)) } + 4x3 + 24x2
evaluate function   
4. Evaluate when f(x) = (x+1)²
a.) f(3)
b.) f(-1)
c.) f(a)
d.) f(x - h)
expression versus equation   
Equation vs. Expression
  • An equation is a sentence.
  • An expression is a phrase, a sentence fragment.
 
  • One solves an equation.
  • One simplifies an expression.
 
Expression, Not Equation Computation Errors
sets   
SETS
1. There exist many ways to say the same thing.
a.) The set of all numbers such that the number is greater than 2.
b.) {x | x > 2}    c.)   d.)
2. Write the following in words. Graph it.
a.) {x | x > -1 and x < 3}
a.) this is also {x | -1 < x < 3}
The symbols [ and ] indicate to include the endpoint.
The symobls ( and ) indicate the endpoint is not included.
3. Vocabulary set    integers
number line    multiples    is greater than
simplify expression   
I. Simplify
1.     (18 ÷ 2) · {[9 · 9 - 1 ÷ 2] - [5 · 20 - ( 7 · 9 - 2)]}
 
2.     8(-4)(-1)(-2)
 
3.     8(-4) -1 -2
 
4.     8(-4 -1(-2))
 
5.     -6 [ -3 - 2(5 - 3)]
 
I. Vocabulary: evaluate    expression
like terms    combine like terms   
II. Simplify the expression.
1.) 3x + 5 - 2x - 4  
2.) 3x² + 5x² - 8x² + 9x²  
3.) x - 2 + x - 6  
IV. Complete the computation.
4.) Add: - 5xy + 3yx  
5.) Multiply: (- 5xy)(3yx)  
6.) Subtract: - 5xy - 3yx  
7.) Divide:
- 5xy
-------
  3yx
 
8.) Square: (- 5xy)²  
9.) Square: (3yx)²  
graphing table   
VIII. Evaluate each expression when x is 0, then 1, then 2, then -1/2.
8. 2x+5
9. -x+3
10. (1/2)x + 1
8. 0, 1, 2, -1/2
9. 5, 7, 9, 4
10. 1, 1 1/2, 2, 3/4
graphing table   
I. Complete the table.
1. y = 4x + 2    
xy
0 
 0
2 
 -3
2. y = -x/4 + 2    
xy
0 
 0
-4 
 10
3. 4x + 6y = 12
xy
0 
 0
1 
 1/2
1. y = 4x + 2      
xy
02
-1/20
210
-5/4-3
 2. y = -x/4 + 2      
xy
02
80
-43
-3210
 3. 4x + 6y = 12
xy
02
30
14/3
9/41/2
evaluate an expression
Comments:
    Above, in section I. when required to evaluate an expression for many values of x, the easiest value of x to use is 0 because 0 times anything is 0 and the term with the zero is eliminated. 
	Ex.	Evaluate 3x + 4 when x is 0 becomes
	3(x) + 4
	3(0) + 4
	4
Answers: I.
a.)
x  3x + 4
-1   1
3   13
2   10
0   4
b.)
x  x/2 + 1
-1   1/2
3   2.5
2   2
0   1
c.)
x  6 - 2x
-1   8
3   0
2   2
0   6


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