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

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