Algebra Formula Bank

This is Algebra Formula Bank. So this Algebra Formula Bank provides all kinds of formula related to Algebra. Hope students find it useful.

Algebra Formula Bank

Here we give algebra formulas in different categories. Let’s see them one by one.

Square formula in Algebra

• a² – b² = (a – b)(a + b)
• (a + b)² = a² + 2ab + b²
• a² + b² = (a – b)² + 2ab
• (a – b)² = a² – 2ab + b²   
• a² + b² = (a + b)² – 2ab

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These are very basic and important formula in Algebra. Though these formulas are basic but they are very important while solving the problems in Algebra.

Square of Three Terms

• (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc
• (a – b – c)² = a² + b² + c² – 2ab – 2ac + 2bc

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The next important category of formula in Algebra is cubic formula. So in this Algebra Formula Bank now we present the formula for cube.

• (a + b)³ = a³ + 3a²b + 3ab² + b³ ; (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)³ = a³ + 3a²b + 3ab² + b³
• (a – b)³ = a³ – 3a²b + 3ab² – b³

Some additional formula in the Algebra

These formulas have no frequent use in school level. However we use them in university level very much.

• (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)

Algebra Formula Collection for advance level

• If n is a natural number, aⁿ – bⁿ = (a – b)(a^n-1 + a^n-2b+…+ b^n-2a + b^n-1)
• If n is even (n = 2k), aⁿ + bⁿ = (a + b)(a^n-1 – a^n-2b +…+ b^n-2a – b^n-1)
• If n is odd (n = 2k + 1), aⁿ + bⁿ = (a + b)(a^n-1 – a^n-2b +…- b^n-2a + b^n-1)
• (a + b + c + …)² = a² + b² + c² + … + 2(ab + ac + bc + ….

Laws of Indices

• Laws of Exponents
  (a^m)(aⁿ) = a^m+n
  (ab)^m = a^mb^m
  (a^m)ⁿ = a^mn
• Fractional Exponents
  a⁰ = 1

In this expression the base a itself can never be zero.

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