Lesson Intermediate Algebra Formulas Review

Source code of 'Intermediate Algebra Formulas Review'

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About sofiyacherni: B.S. in Math from South Dakota School of Mines and Technology

ALGEBRAIC PROPERTIES

Commutative Property:  
{{{a + b = b + a}}}(for addition)
{{{ab = ba}}} (for multiplication)
Associative Property:  
{{{(a + b) + c = a + (b + c)}}}(for addition)
{{{(ab)*c = a*(bc)}}}(for multiplication)
Distributive Property of Multiplication Over Addition:
{{{a*(b + c) = ab + ac}}}
{{{(b + c)*a = ba + ca}}}
Identity Property:
{{{a + 0 = a}}}(for addition)
{{{a*1 = a}}}(for multiplication)

PROPERTIES OF EXPONENTS

Product of Powers
{{{a^m*a^n=a^(m+n)}}}
Power of Power
{{{(a^m)^n=a^(mn)}}}
Power of a Product
{{{(ab)^m=a^m*b^m}}}
Negative Exponent
{{{a^(-m)=1/(a^m)}}} where {{{a<>0}}}
Zero Exponent
{{{a^0=1}}} where {{{a<>0}}}
Quotient of Powers
{{{(a^m)/(a^n)=a^(m-n)}}} where {{{a<>0}}}
Powers of a Quotient
{{{(a/b)^m=(a^m)/(b^m)}}} where {{{b<>0}}}

SLOPES AND INTERCEPTS
If a line passes through points (x1,y1) and (x2,y2) the the slope m is
{{{m=(y2-y1)/(x2-x1)}}}
If a line passes through a point (x1,y1) with a slope m then the equation for that line is
{{{y-y1=m(x-x1)}}} (point-slope form)
If an equation for a line is in a slope-intercept form
{{{y=mx+b}}} then the ordered pair (0,b) is the y-intercept
If an equation for a line is in the form
{{{x=(1/m)y+c}}} then the ordered pair (c,0) is the x-intercept