Question

Formula for algebra
Formula of algebra​

Answer 1

Answer:

Important Formulas in Algebra

Here is a list of 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)(an-1 + an-2b+…+ bn-2a + bn-1)

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

If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)

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

Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn

Answer 2

Step-by-step explanation:

(a + b) 2 = a 2 + b 2 + 2ab

(a − b) 2 = a 2 + b 2 − 2ab

a 2 − b 2 = (a − b) (a + b)

(x + a) (x + b) = x 2 + (a + b) x + ab

(a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca

(a + (−b) + (−c)) 2 = a 2 + (−b) 2 + (−c) 2 + 2a (−b) + 2 (−b) (−c) + 2a (−c)

(a – b – c) 2 = a 2 + b 2 + c 2 − 2ab + 2bc − 2ca

(a + b) 3 = a 3 + b 3 + 3ab(a + b)

(a − b) 3 = a 3 - b 3 - 3ab(a - b)

a 3 − b 3 = (a − b) (a 2 + b 2 + ab)

a 3 + b 3 = (a + b) (a 2 + b 2 − ab)

(a + b + c) 3 = a 3 + b 3 + c 3 + 3(a + b)(b + c)(c + a)

a 3 + b 3 + c 3 − 3abc = (a + b + c) (a 2 + b 2 + c 2 − ab − bc − ac)

If (a + b + c) = 0,

a 3 + b 3 + c 3 = 3abc