Here is a list of Algebraic formulas

Algebraic formulas

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 ; (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
(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)
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 Exponents
(a^m)(aⁿ) = a^m+n(ab)^m = a^mb^m(a^m)ⁿ = a^mn

Fractional Exponents
a⁰ = 1
$\frac{a^{m}}{a^{n}} = a^{m - n}$
$a^{m}$ = $\frac{1}{a^{- m}}$ $a^{- m}$ = $\frac{1}{a^{m}}$

SOLVED EXAMPLES
Question 1: Find out the value of 5² – 3²Solution:
Using the formula a² – b² = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2 $\times$ 8
= 16

Question 2: 4³ $\times$ 4² = ?
Solution:
Using the exponential formula (a^m)(aⁿ) = a^m+nwhere a = 4
4³ $\times$ 4²= 4³⁺²= 4⁵= 1024