Question

Give all important algebraic identities

How to make all algebraic identities.​

Answer 1

Identity I: (a + b)2 = a2 + 2ab + b2. Identity III: a2 – b2= (a + b)(a – b) Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab. Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca. Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)

The standard algebraic identities are: (a + b)2 = a2 + 2ab + b. (a – b)2 = a2 – 2ab + b. a2 – b2 = (a + b)(a – b) (x + a)(x + b) = x2 + (a + b) x + ab. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca. (a + b)3 = a3 + b3 + 3ab (a + b) (a – b)3 = a3 – b3 – 3ab (a –b).

Answer 2

Answer:-

What are  algebraic identities?

Algebraic identities are equalities which remain true  to solve problems in Math. They are  used to rewrite expressions in different ways.

All the Algebraic identities are:-

(a + b)² = a² + 2 ab + b²

 

(a - b)² = (a + b)² - 4 ab

a² - b² = (a + b) (a - b)

 

(x+a) (x+b) =x² + (a + b) x+a b

(a + b)² = (a - b)² + 4 ab

(a - b)² = a² - 2 ab + b²

(a-b)³=a³-3a²b+3ab²-b³

(a-b)³=a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²-ab+b²)

a³-b³= (a-b)(a²+ab+ b²)

a³-b³=(a-b)³ +3ab(a-b)

(a+b+c)²= a²+b²+c² +2ab+2bc+2ca

(a+b-c)²=a²+b²+c² +2ab-2bc-2ca

(a-b+c)²= a²+b²+c²-2ab-2bc+2ca

(a-b-c)²= a²+b²+c²-2ab+2bc-2ca

a² + b² = (a - b)² + 2ab

 (a + b + c)³ = a³ + b³ + c³ + 3a²b + 3a²c + 3ab²+3b²c + 3ac² + 3bc² + 6abc

(a - b - c)³ = a³ - b³ - c³ - 3a²b - 3a²c + 3ab² + 3b²c + 3ac² - 3bc² + 6abc