Algebra Tips and Tricks for Government Exams

• a² – b² = (a – b)(a + b)
• (a+b)² = a² + 2ab + b²
• a² + b² = (a – b)² + 2ab
• (a – b)² = a² – 2ab + b²
• (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc
• (a – b – c)² = a² + b² + c² – 2ab – 2ac + 2bc
• (a + b)³ = a³ + 3a²b + 3ab² + b³ ,
  which can be also denoted as – (a + b)³ = a³ + b³ + 3ab(a + b)
• (a – b)³ = a³ – 3a²b + 3ab² – b³
• a³ – b³ = (a – b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² – ab + b²)
• (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴)
• (a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴)
• a⁴ – b⁴ = (a – b)(a + b)(a² + b²)
• a⁵ – b⁵ = (a – b)(a⁴ + a³b + a²b² + ab³ + b⁴)

Formulas Required  for Solving Coordinate Geometry Questions:

• Distance between two points A(x₁, y₁) and B(x₂, y₂)
  
• Slope of line when two points are given (x₁, y₁) and (x₂, y₂) 
  
• Slope of line when linear equation is given ax + by = c => -a/b
• Midpoint 
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x₁, y₁) and B(x₂, y₂) externally in the ratio m:n is given by 
  
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x₁, y₁) and B(x₂, y₂) externally in the ratio m:n is given by 
  
• Centroid of a triangle with its vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) 
  
• Area of a Triangle with its vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃) 
  
• Division of a line segment by a point
  If a point p(x, y) divides the join of A(x₁, y₁) and B(x₂, y₂), in the ratio m: n, then 
• The equation of a line in slope intercept form is Y= mx+ c, where m is its slope.
  The equation of a line which has gradient m and which passes through the point (x₁, y₁) is =
  y – y₁ = m(x – x₁).