User:Cmanash/sandbox/Base Factor-Lead Factor Theorem

Square of Any Number = Base Factor2 + 2 X Base Factor X Lead Factor+ Lead Factor2 = (BF2) + (2 X BFX LF) + (LF2)

Base Factor = Any number which is easier for further calculation can be considered as the base factor.

Lead Factor = Target Number – Base Factor

Example 1

If you want to find the square of 25 You can take any digit to find the square of 25 If we take 20 as the base factor, Then the calculation will be as follows Base Factor = 20, Lead Factor = Target Figure or Number – Base Factor = 25-20 = 5 =( 20X20)+ (2X 20X5 )+ (5X5) = 400+ 200+25 = 625 Example 2 If we take 10 as the base factor, Then the equation will be Base Factor = 10, Lead Factor = 25-10 = 15 = (10X10) + (2X 10X 15)+ (15X15) =100+300+225 =625. Example 3 If we take 30 as the base factor, Then the calculation will be Base Factor = 30, Lead Factor = 25-30 =(-5) = (30X30) +(2X 30X-5) +(-5X-5) =900-300+25 = 625 Example 4 If we take 50 as base facor, lead factor = 25-50 = -25 =( 50X50) +(2X 50X-25) +(-25X-25) ( Here again simplified approach can be done) = 2500-2500+625 = 625 From the above example, it is cleared that for finding square of any number, finding nearest easy base for calculation is the primary step and based on that lead factor can be arrived. For find cube, the equation will be Square x the number Or Cube =(Base Factor3) + (3X Base Factor2 X Lead Factor) + (3X Base Factor XLead Factor2)+ (Lead Factor3) =(BF3 )+ (3X BF2X LF) + (3X BFx LF2)+ (LF3) For Eg cube of 14 = Base Factor 10, Lead Factor = Target Number – Base Factor = 14-10 Applying the above formulae = ( 10X10X10)+ ( 3X10X10X 4)+(3X10X4X4)+(4X4X4) = 1000+1200+480+64 =2744 Example 2- Cube of 25 Base Factor = 20, Lead Factor 25-20 = 5 Applying the formulae =(BF3 )+ (3X BF2X LF) + (3X BFx LF2)+ (LF3)

= ( 20X20X20) +(3X20X20X5)+(3X20X5X5)+(5X5X5) = 8000+6000+1500+125 =15625.

This formula is a quick and easy approach for finding square, cube or any higher power.