  # Simplifying Algebraic Expressions

constant- represents a quantity that does not change.

examples: 3, 4.8,π

variable- symbol representing a quantity that does

change examples: x, y, a

coefficient- a multiplier

examples:

4x, 4 multiplies x , so 4 is the coefficient of x

3xyz- the coefficient of z is 3xy

algebraic expressions - any combination of constants,

variables and operation symbols

examples: 2x + 45 and algebraic terms parts of an algebraic expression

separated by + or −

examples: 43x is a term, as is xy

How many terms are in the expression ?

Equation- statement that two algebraic expressions

are equal

Example: 5x2 − 3x = xy

Simplifying Algebraic Expressions

Order of Operations :

Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction

(Please Excuse My Dear Aunt Sally)

Example: Simplify Multiplying Algebraic Expressions

For any real numbers a , b, c and d:

a(b + c) = ab + ac
(a + b)(c + d) = ac + ad + bc + bd
note: (a + b)2 = (a + b)(a + b) = a2 + 2ab + b2

“Expand” means “multiply out”

Expand the expression : (x + 4)(x − 2)

Independent Variable- the “input” variable, usually,

but not always, x

Dependent Variable- the “output” variable, depends

on the input, usually, but not always, y

Linear Function - a relation between the independent

and dependent variables characterized by a common

difference or slope

Two important parameters:

start value, or seed (often P0or b)

common difference , or slope (often d or m)

Slope- describes direction and steepness of a line

Positive slope - line increases from left to right

Negative slope- line decreases from left to right Estimate the slope:  Graphing lines using intercepts

x-intercept- function value when y = 0

y-intercept- function value when x = 0

Name intercepts: Graph:x-intercept: -3,
y-intercept: -1. Graphing with slope and y -intercept

Plot the y-intercept.
Use slope to plot another point.

Connect the points, extending the line both

directions.

Example:

Graph a line with y-intercept 1 and slope 3/2: Direct and Indirect Variation

Direct Variation- two variables both increase

proportionally

Indirect Variation-one variable increases, the other

decreases

variation constant- usually k, also called constant of

proportionality

Direct variation is modeled by: y = kx

We say: “y varies directly with x” or “y is directly

proportional to x”

Examples:

• profit and cost of an item

• The distance a spring stretches varies directly as

the amount of weight that is handing on it.

Example: A weight of 50 pounds stretches the spring

10 inches. How much would the spring be stretched

with a weight of 60 pounds?

direct variation, so use y = kx

Let y by the distance, and x be the weight.

10 = k · 50 or k = 1/5

Model: y = (1/5)x

y = (1/5) · 60 = 12

A 60 pound weight will stretch the spring 12 inches.

Indirect variation modeled by: y = k/x

We say “y varies indirectly with x” or “y is indirectly

proportional to x”

Examples:

• time in dorms and appeal of dorm food

• wing beats and wing length

Example: Herring gull- 24 centimeter long wings

beat 3 times per second

assume variation constant remains the same

How fast will 12 centimeter wings beat?

Let y represent the wing beats and x represent the

length of the wing.

Indirect variation, so use y = k/x

3 = k/24 or 3(24) = k = 72

Model: y = 72/x

y = 72/12 = 6

A bird with wing length 12 centimeters will beat 6

times per second.

Solving Literal Equations

Consider y is determined by the value assigned to x. Call x the

independent variable, and y the dependent variable.

Change the roles of dependent and independent by

solving for x:

(remember that the equation must balance, what

happens on one side must happen on the other also) Prev Next

Start solving your Algebra Problems in next 5 minutes!   Algebra Helper Download (and optional CD) Only \$39.99 Click to Buy Now: OR   2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of June 22nd you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor: Step 2 : Let Algebra Helper solve it: Step 3 : Ask for an explanation for the steps you don't understand: Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!   Algebra Helper Download (and optional CD) Only \$39.99 Click to Buy Now: OR   2Checkout.com is an authorized reseller
of goods provided by Sofmath "It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..." C. Sievert, KY Sofmath 19179 Blanco #105-234San Antonio, TX 78258 Phone: (512) 788-5675Fax: (512) 519-1805 Home   : :   Features   : :   Demo   : :   FAQ   : :   Order Copyright © 2004-2021, Algebra-Answer.Com.  All rights reserved.