Learn the Identities for Solving Problems related to Simplification of a Decimals. Check out the Solved Examples on simplifying Expressions with Decimals and get to know the concept better. You can apply these Identities and simplify the expressions involving decimals. Refer to the step-by-step explanation provided below for solving or simplifying expressions involving decimals.

Identities used in the Simplifying Expressions with Decimals are provided as such

(a)Â (a + b)^{2}Â = a^{2}Â + b^{2}Â + 2ab

(b)Â (a – b)^{2}Â = a^{2}Â + b^{2}Â – 2ab

(c)Â a^{2}Â – b^{2}Â = (a + b) (a – b)

(d)Â a^{3}Â + b^{3}Â = (a + b) (a^{2}Â – ab + b^{2})

(e)Â a^{3}Â – b^{3}Â = (a – b) (a^{2}Â + ab + b^{2})

## How to Simplify Decimal Expressions?

Follow the simple and easy process listed below to simplify the decimal expressions. They are in the below fashion

- Check the given expression and observe which identity is close to it.
- Simplify the expressions to the possible extent.
- Later substitute the given values accordingly and then simplify according to the order of operations to obtain the result.

Also, Read:

### Worked Out Examples on Simplifying Expressions Involving Decimals

**1. Simplify the Expression {(0.8 – 0.5 ^{2}}/{(0.8)^{2} – 2(0.8)(0.5) + (0.5)^{2}}?**

Solution:

Given Expression is {(0.8 – 0.5)^{3}}/{(0.8)^{2} – 2(0.8)(0.5) + (0.5)^{2}}

Let us consider a = 0.8, b = 0.5

Thus, it becomes {(a-b)^{3}}/{(a^{2} -2ab+b^{2})}

= {(a-b)^{3}}/{(a-b)^{2}}

= a-b

Now, substitute the values of a, b in the simplified expression

= 0.8-0.5

= 0.3

Thus, {(0.8 – 0.5^{2}}/{(0.8)^{2} – 2(0.8)(0.5) + (0.5)^{2}} simplified results in the value 0.3

**2.** **Simplify the expression [(4.8) ^{3} – (2.4)^{3}]/[(4.8)^{2} + (2.4)^{2} – 2(4.8)(2.4)]?**

Solution:

Given Expression is [(4.8)^{3} – (2.4)^{3}]/[(4.8)^{2} + (2.4)^{2} – 2(4.8)(2.4)]

Let us consider a = 4.8, b = 2.4

Now, rearranging the expression using the Identities we know we get

= [a^{3}Â – b^{3}]/[a^{2}Â – 2ab + b^{2}]

= Â [~~(a – b)~~Â (a^{2}Â + ab + b^{2})]/[~~(a – b)~~^{2}]

= (a^{2}Â + ab + b^{2})/(a-b)

Placing the value of a, b we have the equation as follows

= (4.8)^{2}+(4.8)(2.4)+(2.4)^{2}}/(4.8-2.4)

= (23.04+11.52+5.76)/2.4

= 40.32/2.4

= 16.8

Therefore, [(4.8)^{3} – (2.4)^{3}]/[(4.8)^{2} + (2.4)^{2} – 2(4.8)(2.4)] results the value 16.8

3. Simplify the Expression [(7.65)^{2} – (3.35)^{2}]/(7.65 + 3.35)

Solution:

Given Expression is [(7.65)^{2} – (3.35)^{2}]/(7.65 + 3.35)

Let us consider a = 7.65, b = 3.35

Now, rearranging the expression using the Identities we know we get

= [a^{2} -b^{2}]/(a+b)

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

= a-b

Placing the value of a, b we have the equation as follows

= 7.65-3.35

= 4.3

Therefore, on simplifying [(7.65)^{2} – (3.35)^{2}]/(7.65 + 3.35) we get 4.3

**4. Simplify [(7.8) ^{3} + (2.2)^{3}]/[(7.8)^{2} + (2.2)^{2}-(7.8)(2.2)]?**

Solution:

Given Expression is [(7.8)^{3} + (2.2)^{3}]/[(7.8)^{2} + (2.2)^{2}-(7.8)(2.2)]

Let us consider a = 7.8, b = 2.2

Now, rearranging the expression using the Identities we know we get

= [a^{3}+b^{3}]/[a^{2}-ab+b^{2}]

= [(a+b)~~(a~~]/^{2}-ab+b^{2})~~a~~)^{2}-ab+b^{2}

= a+b

Placing the value of a, b we have the equation as follows

= 7.8+2.2

= 10

Therefore, [(7.8)^{3} + (2.2)^{3}]/[(7.8)^{2} + (2.2)^{2}-(7.8)(2.2)] on simplification results in the value 10.