# Simplified value of ${(1.25)^3} - 2.25{(1.25)^2} + 3.75{(0.75)^2} - {(0.75)^3} = $

(A) $\dfrac{1}{2}$

(B) $\dfrac{1}{4}$

(C) $\dfrac{1}{8}$

(D) $\dfrac{1}{3}$

Last updated date: 25th Mar 2023

•

Total views: 206.7k

•

Views today: 3.84k

Answer

Verified

206.7k+ views

**Hint:**In order to solve this question, to simplify the given expression, first we will try to simplify the expression as in the form of any algebraic expression, that makes the simplification simple and clear. Or, we can also solve it by using the BODMAS rule.

**Complete step-by-step solution:**

The given expression: ${(1.25)^3} - 2.25{(1.25)^2} + 3.75{(0.75)^2} - {(0.75)^3}$

Firstly, we will try to simplify the expression as in the form of any algebraic expression, that makes the simplification simple and clear.

$= {(1.25)^3} - 3 \times 0.75 \times {(1.25)^2} + 3 \times 1.25 \times {(0.75)^2} - {(0.75)^3} $

If we see the above expression we can write this as an algebraic expression in variable a, b as:

${a^3}-3\times a \times b^2+ 3\times {a^2} \times b -b^3 = \left(a-b\right)^{3}$

Thus on comparing we get,

$= {(1.25 - 0.75)^3}$

$= {(0.5)^3} = {(\dfrac{1}{2})^3} = \dfrac{1}{8} $

Or, we can also solve this question without making the expression simple-

We will solve the given question, by the BODMAS Rule:-

$= {(1.25)^3} - 2.25{(1.25)^2} + 3.75{(0.75)^2} - {(0.75)^3} $

$= 1.95 - 2.25(1.56) + 3.75(0.56) - 0.42 $

$= 1.95 - 3.51 + 2.1 - 0.42$

$= 0.96$

**Hence, the correct option is (C) $\dfrac{1}{8}$ .**

**Note:**In BODMAS Rule, first we will start working with the bracket contents, and then we will do divide, multiply, addition and subtraction respectively. This rule can be used in every sector of mathematics.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?