Lesson Intermediate Algebra Formulas Review

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This Lesson (Intermediate Algebra Formulas Review) was created by by sofiyacherni(99) About Me : View Source, Show
About sofiyacherni: B.S. in Math from South Dakota School of Mines and Technology
ALGEBRAIC PROPERTIES
Commutative Property:
a+%2B+b+=+b+%2B+a(for addition)
ab+=+ba (for multiplication)
Associative Property:
%28a+%2B+b%29+%2B+c+=+a+%2B+%28b+%2B+c%29(for addition)
%28ab%29%2Ac+=+a%2A%28bc%29(for multiplication)
Distributive Property of Multiplication Over Addition:
a%2A%28b+%2B+c%29+=+ab+%2B+ac
%28b+%2B+c%29%2Aa+=+ba+%2B+ca
Identity Property:
a+%2B+0+=+a(for addition)
a%2A1+=+a(for multiplication)

PROPERTIES OF EXPONENTS
Product of Powers
a%5Em%2Aa%5En=a%5E%28m%2Bn%29
Power of Power
%28a%5Em%29%5En=a%5E%28mn%29
Power of a Product
%28ab%29%5Em=a%5Em%2Ab%5Em
Negative Exponent
a%5E%28-m%29=1%2F%28a%5Em%29 where a%3C%3E0
Zero Exponent
a%5E0=1 where a%3C%3E0
Quotient of Powers
%28a%5Em%29%2F%28a%5En%29=a%5E%28m-n%29 where a%3C%3E0
Powers of a Quotient
%28a%2Fb%29%5Em=%28a%5Em%29%2F%28b%5Em%29 where b%3C%3E0

SLOPES AND INTERCEPTS
If a line passes through points (x1,y1) and (x2,y2) the the slope m is
m=%28y2-y1%29%2F%28x2-x1%29
If a line passes through a point (x1,y1) with a slope m then the equation for that line is
y-y1=m%28x-x1%29 (point-slope form)
If an equation for a line is in a slope-intercept form
y=mx%2Bb then the ordered pair (0,b) is the y-intercept
If an equation for a line is in the form
x=%281%2Fm%29y%2Bc then the ordered pair (c,0) is the x-intercept

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