In this page algebra formulas we are going to see formulas
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.
Example:
Simplify (x + 8) (x + 8)
Solution:
For simplifying this we have to multiply (x + 8) by x and (x + 8) by 8.
(x + 8) (x + 8) = x² + x (8) + 8 (x) + 8 (8)
= x² + 8 x + 8 x + 64
= x² + 16 x + 64
Alternate method using formula
(x + 8) (x + 8) = (x + 8)²
without writing (x + 8) twice we can write (x + 8) (x + 8) as (x + 8)². Now we are going to compare this with the formula (a + b)² = a² + 2 a b + b². By comparing (x + 8) with the formula we will get "x" instead of "a" and we will get "8" instead of "b".
(x + 8)² = x² + 2 (x) (8) + 8²
= x² + 16 x + 64
Formulas 
Examples & Practice questions 
(1) (a + b)² = a² + 2 ab + b²  
(2) (a  b)² = a²  2 ab + b²  
(3) a²  b² = (a + b) (a  b)  
(4) (x+a)(x+b) =x² + (a + b) x+a b  
(5) (a+b)³=a³+3a²b+3ab²+b³  
(6)(ab)³=a³ 3 a²b+3 a b²  b³  
(7) (a³+b³)= (a+b)(a²ab+b²)  
(8) (a³b³)=(ab)(a²+ab+ b²) 
(9) (a+b+c)²= a²+b²+c² +2ab+2bc+2ca
 
(12) a³+b³=(a+b)³3 ab (a + b)  
(13) a³b³=(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(ab)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 
(20) Quadratic equation =  b ± √(b²  4 a c)/2a 
(20) General form of Quadratic equation x²  (α + β) x + αβ = 0. α + β = Sum of roots α β = Product of roots 
(21) Nature of roots ∆ > 0 but not a perfect square ∆ > 0 but a perfect square
∆ = 0 ∆ < 0 but a perfect square 
Real,unequal and irrational
Real, equal and rational

(22) Relationship between roots and coefficients Sum of roots α + β = b/a Product of roots α β = c/a 

(22) Cross multiplication methods 