Students,
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Mrs. Pauley

Algebra Formulas  

Quadratic Formula
In an equation like ax2 + bx + c = 0, you can solve for x using the Quadratic Formula shown on the left.

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)

Absolute Value

•  |x| < a   if and only if   -a<x<a
  
•  |x| > a   if and only if either x>a or x<-a
  

Special Product Formulas

• (x + y)(x – y) = x2 – y2
  
• (x + y) 2 = x2 + 2xy + y2 
• (x – y) 2 = x2 – 2xy + y2
  
• (x + y)3 = x3 + 3xy2 + 3xy2 + y3   
• (x – y) 3 = x3 – 3xy2 + 3xy2 – y3 
  

Special Factoring Formulas

• x2 – y2 = (x + y)(x – y)
  
• x2 + 2xy + y2 = (x + y)2
• x2 – 2xy + y2 = (x – y) 2
  
• x3 – y3 = (x – y)(x2 + xy + y2)
• x3 + y3 = (x + y)(x2 – xy + y2)
  

Inequalities

• If a>b and b>c, then a>c.
  
• If a>b, then a+c>b+c.
  
• If a>b and c>0, then ac>bc.
  
• If a>b and c<0, then ac<bc.
  

Word Problem Formulas

•  Distance = rate x time
  
•  Rate = distance/time
  
•  Time = distance/rate
  

Laws of Exponents

• (am)(an) = am+n
  
• (ab)m = ambm
• (am)n = amn
• a0 = 1
• (am)/(an) = am-n
• a-m= 1/(am)

Exponents and Radicals

• axay = ax + y 
  
• a1/x = x√a
  
• (ax)y  = axy 
  
• ax/y = y√ax 
  
• (ab)x = axbx
  
• ax/y = ( y√a)x 
  
• (a/b)x = ax/bx   
  
• x√ab = x√a x√b
  
• ax/ay = ax-y
  
• x√(a/b) = x√a/x√b
  
• a-x = 1/ax                     
  
• x√y√a = xy√a
  

 

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Perfect Squares