Some Useful Algebra Formulas

Just remembering Algebra (math) formulas are not going to help you to crack any examinations, one should have the ability to execute these formulas in the exam hall. To do that, one has to practice the various types of algebraic math problems repeatedly.

Some Important Formulas of Algebra

Square Formula

• 01 (x+y)² = (x+y)(x+y) = x²+2xy+y²
• 02 (x-y)² = (x-y)(x-y) = x²-2xy+y²
• 03 (x+y)² = (x-y)² + 4xy
• 04 (x-y)² = (x+y)² – 4xy
• 05 x²-y² = (x+y)(x+y)
• 06 (x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yx
• 07 4xy = [ (x+y)² – (x-y)² ]
• 08 2( x²+y²) = [ (x+y)² + (x-y)² ]
  

Cube Formula

• 01 (x + y)³ = x³ + 3x²y + 3xy² + y³
• 02  (x + y)³ = x³ + y³ + 3xy(x + y)
• 03  (x – y)³ = x³ – 3x²y + 3xy² – y³
• 04  (x – y)³ = x³ – y³ – 3xy(x – y)
• 05  x³ + y³ = (x + y)(y² – xy + y²)
• 06  x³ – y³ = (x – y)(x² + xy + y²)
• 07  (x + y)⁴ = x⁴ + 4x³y + 6x²
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  y² + 4xy³ + y⁴)
• 08  (x – y)⁴ = x⁴ – 4x³y + 6x²y² – 4xy³ + y⁴)
• 09  x⁴ – y⁴ = (x² + y²)(x + y) (x – y)
• 10  x³ + y³ + z³ – 3xyz = (x + y + z)( x² + y² + z² -xy – yz – zx)
  

Laws of Exponent

• 01  x^m × xⁿ = x^m+n
• 02  x^m / xⁿ = x^m-n
• 03  (xy)^m = x^m × y^m
• 04  (x^m)ⁿ = x^mn
• 05  x^m = (1/x^-m)
• 06  x⁰ = 1
• 07 √x = x^½
• 08 ³√x = x^¹/³

‘Quadratic Formula :

01 If a Quadratic Equation is ax² + bx + c = 0 ; Then the roots of this equation are –

The formula of Irrational number

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Algebra Formulas are very important for mathematics as well as science. If you are an aspirant of competitive exams like SSC, CGL, Rail NTPC, Police, Defence, etc. then you should remember all the formulas.