Here is a list of Algebraic formulas
Algebraic formulas

a^{2} – b^{2} = (a – b)(a + b)

(a+b)^{2} = a^{2} + 2ab + b^{2}

a^{2} + b^{2} = (a – b)^{2} + 2ab

(a – b)^{2} = a^{2} – 2ab + b^{2}

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2ac + 2bc

(a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2ab – 2ac + 2bc

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} ; (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)

(a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}

a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})

a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

(a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}

(a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4})

(a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4})

a^{4} – b^{4} = (a – b)(a + b)(a^{2} + b^{2})

a^{5} – b^{5} = (a – b)(a^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4})

If n is a natural number, a^{n} – b^{n} = (a – b)(a^{n1} + a^{n2}b+…+ b^{n2}a + b^{n1})

If n is even (n = 2k), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +…+ b^{n2}a – b^{n1})

If n is odd (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +… b^{n2}a + b^{n1})

(a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + ….