# Simplification of Decimal

Use the identities to solve the problems based on simplification of decimal. We will make use of these identities in some of the questions related to division of decimals.

Learn the following identities to apply these in simplifying decimal.

(a) (a + b)2 = a2 + b2 + 2ab

(b) (a - b)2 = a2 + b2 - 2ab

(c) a2 - b2 = (a + b) (a - b)

(d) a3 + b3 = (a + b) (a2 - ab + b2)

(e) a3 - b3 = (a - b) (a2 + ab + b2)

Worked-out examples on simplification of decimal:

Let us observe how to simplify decimals using identities with detailed step-by-step explanation.

Simplify the following:

(a) {(0.9 - 0.6)2}/{(0.9)2 - 2(0.9)(0.6) + (0.6)2}

Solution:

Let, a = 0.9 and b = 0.6

So, [(a - b)3]/[a2 - 2(a)(b) + b2]

= (a - b)3/(a - b)2

= (a - b)

Now putting the value of a and b we get,

= 0.9 - 0.6

= 0.3

(b) [(5.8)3 - (2.6)3]/[(5.8)2 + (2.6)2 - 2(5.8) + (2.6)2]

Solution:

Let a = 5.8 and b = 2.6

So, we have

= [a3 - b3]/[a2 - 2ab + b2]

= [(a - b) (a2 + ab + b2)]/[(a - b)2]

= (a2 + ab + b2)/(a - b)

Now putting the value of a and b we get,

= [(5.8)2 + (5.8)(2.6) + (2.6)2]/(5.8 - 2.6)

= 55.48/3.2

= (55.48 × 10)/(3.2 × 10), Multiply both numerator and denominator by 10

= 554.8/32

= 17.3375

(c) [(8.65)2 - (4.35)2]/(8.65 - 4.35)

Solution:

Let a = 8.65 and b = 4.35

So, we have

= [a2 - b2]/(a - b)

= [(a + b)(a-b)]/(a - b)

= a + b

Now putting the value of a and b

= 8.65 + 4.35

= 13

Related Concept

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles 1. ### Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

Dec 04, 23 02:14 PM

Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

2. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Dec 04, 23 01:50 PM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…