Very Useful Algebric Formula in Mathematics

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⇜Very Important Formulas in Algebra⇝

Below is the list of Algebraic formulas👇

·         (a + b)² =(a + b) (a + b)= a² + 2ab + b²

·         a² – b² = (a – b) (a + b)

·         a² + b² = (a + b)² – 2ab

·         (a – b)² = (a - b) (a - b)=a² – 2ab + b²

·         (a + b + c)² =(a + b + c) (a + b + c)= a² + b² + c² + 2ab + 2bc + 2ca

·         (a – b – c)² =(a - b - c) (a - b - c)= a² + b² + c² – 2ab + 2bc – 2ca

·         (a + b)³ =(a + b) (a + b) (a + b)=  a³ + 3a²b + 3ab² + b³

·         (a + b)³ = a³ + b³ + 3ab(a + b)

·         (a – b)³ =(a – b) (a – b) (a – b)= a³ – 3a²b + 3ab² – b³ = a³ – b³ – 3ab(a – b)

·         a³ – b³ = (a – b) (a² + ab + b²)

·         a³ + b³ = (a + b) (a² – ab + b²)

·         (a + b)⁴ =(a + b) (a + b) (a + b) (a + b) =  a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

·         (a – b)⁴ =(a – b) (a – b) (a – b) (a – b) =  a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴

·         a⁴ – b⁴ = (a – b) (a + b) (a² + b²)

·         a⁵ – b⁵ = (a – b) (a⁴ + a³b + a²b² + ab³ + b⁴)

If n is a natural number aⁿ – bⁿ = (a – b) (a^n-1 + a^n-2b+…+ b^n-2a + b^n-1)

If natural number n is even (n = 2k), aⁿ + bⁿ = (a + b) (a^n-1 – a^n-2b +…+ b^n-2a – b^n-1)

If natural number n is odd (n = 2k + 1), aⁿ + bⁿ = (a + b) (a^n-1 – a^n-2b +a^n-3b²…- b^n-2a + b^n-1)

(a + b + c + …)² = a² + b² + c² + … + 2(ab + ac + bc + ….)

Laws of Exponents

·         (a^m) (aⁿ) = a^m+n 

·         (ab)^m = a^mb^m 

·         (a^m)ⁿ = a^mn

Factorials

·         n! = (1).(2).(3)…..(n − 1).n

·         n! = n(n − 1)! = n(n − 1)(n − 2)! = ….

·         0! = 1

I hope you have received best knowledge by this Post. Thank you for Reading 😊🙏