
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) $\dfrac{1}{3}$
Answer
411.9k+ 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.
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
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Trending doubts
Which king started the organization of the Kumbh fair class 8 social science CBSE

State the differences between manure and fertilize class 8 biology CBSE

The first matrimonial alliance with the Rajput was class 8 social science CBSE

Application to your principal for the character ce class 8 english CBSE

When will we use have had and had had in the sente class 8 english CBSE

Distinguish between SouthWest and NorthEast monsoo class 8 social science CBSE
