ALGEBRAIC IDENTITIES

On this webpage algebraic identities,we are going to see list of identities.

What is Algebraic identity?

An identity is an equality that remains true regardless of the values of any variables that appear within it.

Definition of Formula:

Formula is the short cut of doing problems without formula. It is very long process of doing any problem without formula. Let us consider the following example to understand the purpose of formulas in math.


Formulas

Examples & Practice questions


(1) (a + b)² = a² + 2 ab + b²

Examples

practice questions

(2) (a - b)² = a² - 2 ab + b²

Examples

Practice Questions

(3) a² - b² = (a + b) (a - b)

Examples

Practice Questions

(4) (x+a)(x+b) =x² + (a + b) x+a b

Examples

Practice Questions

(5) (a+b)³=a³+3a²b+3ab²+b³

Examples

Practice Questions

(6)(a-b)³=a³- 3 a²b+3 a b² - b³

Examples

Practice Questions

(7) (a³+b³)= (a+b)(a²-ab+b²)

Examples

Practice Questions

(8) (a³-b³)=(a-b)(a²+ab+ b²)

Examples

Practice Questions

(9) (a+b+c)²= a²+b²+c² +2ab+2bc+2ca


(10) (a-b+c)²=a²+b²+c² -2ab-2bc+2ca


(11) (a-b-c)²= a²+b²+c²-2ab+2bc-2ca


Examples

Practice Questions

(12) a³+b³=(a+b)³-3 ab (a + b)

(13) a³-b³=(a - b)³ + 3 ab (a - b)

(14) a² + b² = (a + b)² - 2ab

(15) a² + b² = (a - b)² + 2ab

(16) a²+b²=½ [(a+b)²-(a-b)²]

(17) ab=¼[(a+b)²- (a - b)²]

(18) (a - b)² = (a + b)² - 4 ab

(19) (a + b)² = (a - b)² + 4 ab

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