Chapter 5Algebra Fundamentals:

Algebraic Terms, Roots, and Powers

Numbers, Expressions, and Terms

• Literal and Real Numbers Real Numbers

•Always have the same value. Never can have other values. Aka. Constants

•Examples: 6, 7, 27,1024, etc.

Literal Numbers•Take on different values

Can represent constants or variables

•Examples: E= I * R

Numbers, Expressions, and Terms

• Algebraic Expressions and Terms Expressions contain Real, Literal, or both types of numbers

Terms are numbers separated by ‘+’ and ‘-’ •2ab + 4c – 5ac

Three terms: 2ab, 4c, 5ac

•Expression with one term – monomial•Expression w/two + terms - polynomial

Numbers, Expressions, and Terms

• Coefficients Of Algebraic term is real number part of term•6 is coefficient of 6xy•Coefficient of ax is ‘1’

• Exponents 53 = 5 * 5 * 5 = 125 X3 = X * X * X = depends on value of X

Finding Values of Algebraic Expressions

• When expression has real and literal numbers Need value of literals to find value 6X2 yields different values for different X’s•If X =3 => 6 * 32 = 6 * 9 = 54•If X =4 => 6 * 42 = 6 * 16 = 96•If X =1 => 6 * 12 = 6 * 1 = 6

If x = 3 and y = 4 Find:•xy = 3 * 4 = 12•x2y = 32 * 4 = 9 * 4 = 36

Finding Values of Algebraic Expressions

• When expression has real and literal numbers If x = 3 and y = 4 Find:

•x2y2 = 32 * 42 = 9 * 16 = 144•4x3y2 = 4 * 33 * 42 = 1730•(xy) 2 = (3 * 4) 2 = 12 2 = 144•(xy) 2 = x 2 y 2 = 3 2 * 4 2 = 9 * 16 = 144

•3x 2 y – xy 2 = 3 * 3 2 *4 – 3 * 4 2 = 108 -48 = 60

Roots

Roots

DC Circuit Examples• In Electronics Literal number in equations represent relationships between variables in electrical circuits. Ohm’s Law E = I * R

•Voltage across a component = Current through the component time resistance of the component

•Example problems 5-7 through 5-11 on page 116

Practice exercises – Practice Problems 5-5 on page 117

AC Circuit Examples

AC Circuit Examples• Impedance of a circuit

Includes resistance and any reactance• Resistance and reactance are orthogonal • i.e. an impedance of circuit with 5 ohms resistance and 5 ohms reactance in series has an impedance of the vector sum of the two elements

Z = (52 +52)1/2 = 501/2 = 7.07 (rounded to 3 places)

Z = 21/2 * 5

• Example 5-14 on page 119

Work Practice problems

• For this and all the chapters Odd number ones have answers in back of book

WORK THEM UNTIL YOU UNDERSTAND THE PROBLEMS