Elementary algebra
Basic Aglebra
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Basics of Algebra Algebra is a division of mathematics designed to help solve certain types of problems quicker and easier. Algebra is based on the concept of unknown values called variables, unlike arithmetic which is based entirely on known number values. This lesson introduces an important algebraic concept known as the Equation. The idea is that an equation represents a scale such as the one shown on the right. Instead of keeping the scale balanced with weights, numbers, or constants are used. These numbers are called constants because they constantly have the same value. For example the number 47 always represents 47 units or 47 multiplied by an unknown number. It never represents another value.
learning algebra
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Solving Systems by Substitution
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A good way to solve systems of equations is by substitution. In this method, you solve on equation for one variable, then you substitute that solution in the other equation, and solve. Example:
1. Problem: Solve the following system:
x + y = 11
3x - y = 5
Solution: Solve the first equation for y
(you could solve for x - it
doesn't matter).
y = 11 - x
Now, substitute 11 - x for y
in the second equation. This gives
the equation one variable, which
earlier algebra work has taught
you how to do.
3x - (11 - x) = 5
3x - 11 + x = 5
4x = 16
x = 4
Two step equations and inequalities
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It takes two steps to solve an equation or inequality that has more than one operation:
Simplify using the inverse of addition or subtraction.
Simplify further by using the inverse of multiplication or division.
Remember, when you multiply or divide an inequality by a negative number, you must reverse the inequality symbol.
Quadratic Equations
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Quadratic Equations
This is what a "Standard" Quadratic Equation looks like:
•The letters a, b and c are coefficients (you know those values). They can have any value, except that a can't be 0.
•The letter "x" is the variable or unknown (you don't know it yet)
Here is an example of one:
The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2).
It is also called an "Equation of Degree 2" (because of the "2" on the x)
More Examples of Quadratic Equations:
In this one a=2, b=5 and c=3
This one is a little more tricky:
•Where is a? In fact a=1, as we don't usually write "1x2"
•b = -3
•And where is c? Well, c=0, so is not shown.
Algebra laws
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history of algebra
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The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.
Algebra Formulas
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Laws of Exponents
(am)(an) = am+n
(ab)m = ambm
(am)n = amn
a0 = 1
(am)/(an) = am-n
a-m= 1/(am)
Quadratic Formula
In an equation like ax2 + bx + c = 0
You can solve for x using the Quadratic Formula:
Binomial Theorem
(a + b)1 = a + b
(a + b)2 = a2 + 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 ...and so on...
Difference of Squares
a2 - b2 = (a - b)(a + b)
Rules of Zero
0/x = 0 where x is not equal to 0.
a0 = 1
0a = 0
a*0 = 0
a/0 is undefined (you can't do it)
Slope and y-intercept.
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Every straight line can be represented by an equation: y = mx + b. The coordinates of every point on the line will solve the equation if you substitute them in the equation for x and y.
The slope m of this line - its steepness, or slant - can be calculated like this:
m = change in y-value
change in x value
Help from math.com
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