simplification copyrighted © by t. darrel westbrook

Simplification

Copyrighted © by T. Darrel Westbrook

26 August 2010 Alg2_Simplification.pptCopyrighted © T. Darrel Westbrook

2

Simplification

What to Simplify?

In this lesson you will learn


3

Simplification

All FractionsAre Reduced

What toSimplify?

DenominatorCan’t Have

ComplexNumbers

RadicalNumbers

RationalNumbers

NegativeNumbers

CombineLike Terms

No NegativeExponents

Index of AllRadicals as Small

As Possible

All ParenthesisRemoved


4

Simplification

Why is x2 and x two different terms?How about x and y?What is a term?SimplifyAre 5 and –13 like terms?

CombineLike Terms

3x2 + 2x – 5 – x2 + 7 = y 4x2 + 2x + 2 = y3x2 + 2x – 5 + 7 = f(x) – 2x2 + 3x 5x2 – x – 5 = f(x)g(x) = 4x – 3x = 3x – 5 + 7 g(x) = 3x – x + 7


5

Simplification

All ParenthesisRemoved

(2x – 3) = f(x) 2x – 3 = f(x)f(x) = – 5(2x – 3) f(x) = – 10x + 15h(x) = – (4x – 7) h(x) = – 4x + 7g(x) = x2 + 3x – (4x2 – 7) g(x) = – 4x2 + 3x + 7


6

Simplification

No NegativeExponents

2–4x –3 + x = k(x)1

24

1

16=x31

x3 + x = 1

x3 + = x4

x3

1 + x4

x3

1

x –3


7

Simplification

22 3 23=24/8 = 2 ½ = 2a4/6 = a2/3 = a23

Index of AllRadicals as Small

As Possible

12248a46


8

Simplification

All FractionsAre Reduced

3

6

1

2

7x

6

x

4+ = g(x)14x

12

3x

12+ = = g(x)17x

12k(x) = –1/2 x +6/4 x – 4 k(x) = x – 4


9

Simplification

DenominatorCan’t Have

ComplexNumbers

RadicalNumbers

RationalNumbers

NegativeNumbers

No Fractions

In Denominator

x5/6

Numbers of the Form

a + bi

3– 2 + 5i

3

2x – 9

No Negative

Numbers In

Denominator

3–2

Numbers

of the Form1a

How to eliminate complex and radicals from the denominator will be discussed in a later lesson.


10

Simplification

Expressions, equalities, or inequalities all follow the same simplification process. Simplification and Order of Operations adds deterministic structure to mathematics (means there is no

ambiguity).

This means that if you and another student of mathematics work the same problems containing grouping symbols and operators,

you both will get the same answer (assuming, of course, you made no simplification, arithmetic, or Order of Operations

errors).


11

Simplification

END OF LINE

simplification copyrighted © by t. darrel westbrook

Documents