ALGEBRA FORMULAS





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

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

(20) Quadratic equation

= - b ± √(b² - 4 a c)/2a

Solving Equations


(20) General form of Quadratic equation

x² - (α + β) x + αβ = 0.

α + β = Sum of roots

α β = Product of roots


Examples

Practice question


(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,unequal and rational


Real, equal and rational


Unreal (imaginary)

Examples

Practice questions


(22) Relationship between roots and coefficients

Sum of roots α + β = -b/a

Product of roots α β = c/a


Examples

Practice questions


(22) Cross multiplication methods


Examples

Practice questions






(a + b)² = a² + 2 ab + b²

(a - b)² = a² - 2 ab + b²

a² - b² = (a + b) (a - b)

(x+a)(x+b)=x²+(a+b)x+ab

(a+b)³=a³+3a²b+3ab²+b³

(a-b)³=a³-3a²b+3ab²-b³

(a³+b³)= (a+b)(a²-ab+b²)

(a³-b³)=(a-b)(a²+ab+ b²)

(a+b+c)²= a²+b²+c²+2ab+2bc+2ca