Question

Write the value of \[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3}\].

Answer 1

Hint: We have to find the value of the given expression \[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3}\]. We solve this question using the concept of cubes of natural numbers and the concept of BODMAS . We should have the knowledge of how to find the cube of a number. First, we will cube the three numbers separately and then using the concept of BODMAS , we will solve the expression after substituting the value of the cubes of the numbers .

Complete step by step answer:
Given :
The value of the expression \[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3}\]
Now, as we know that for the value of the expressions of cubes we can write the expression as :
\[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3} = \left( {30 \times 30 \times 30} \right) + \left( {20 \times 20 \times 20} \right) - \left( {50 \times 50 \times 50} \right)\]
On multiplication of the numbers, we can write the expression as :
\[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3} = \left( {27000} \right) + \left( {8000} \right) - \left( {125000} \right)\]
Now , we also know that the concept of BODMAS states that the addition of terms takes place first then the subtraction takes place .
So , using the concept of BODMAS , we can write the expression as :
\[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3} = \left( {35000} \right) - \left( {125000} \right)\]
On further solving , we get the value of the expression as :
\[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3} = - 90000\]

Hence , we get the value for the given expression \[{\left( {30} \right)^3} + {\left( {20} \right)^3} - {\left( {50} \right)^3}\] as \[ - 90000\].

Note:
The concept of BODMAS states that we will start solving any expression in the following order only .i.e. first the BRACKETS , then the ORDERS, then the DIVISION ,then the MULTIPLICATION ,then the ADDITION , and at last the SUBTRACTION .
We can also solve this question using the concept of the formula of the sum of cubes of two numbers or the formula of the difference of the cubes of two numbers. We will simplify the terms using the formula as given below :
\[{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)\] or \[{a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + {b^2} + ab} \right)\]