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# 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
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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.