Answer
Verified
409.8k+ views
Hint: Here, we will expand the given expression in the form of an algebraic identity. Then by using the suitable algebraic identity we will simplify the expression and by using the BODMAS rule, we will find the value of the algebraic expression.
Formula used:
The cube of the difference of two numbers is given by an algebraic identity \[{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\].
Complete Step by Step Solution:
We are given an arithmetic expression \[{\left( {998} \right)^3}\].
Now, we will rewrite the given expression, which will be in the form of an Algebraic Identity, we get
\[{\left( {998} \right)^3} = {\left( {1000 - 2} \right)^3}\]
Thus, the expanded algebraic expression is in the form of an algebraic identity as \[{\left( {a - b} \right)^3}\] .
Now, by using an algebraic identity \[{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\], we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = {\left( {1000} \right)^3} - 3{\left( {1000} \right)^2}\left( 2 \right) + 3\left( {1000} \right){\left( 2 \right)^2} - {\left( 2 \right)^3}\]
Applying the exponent on the terms, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 1000000000 - 3\left( {1000000} \right)\left( 2 \right) + 3\left( {1000} \right)\left( 4 \right) - \left( 8 \right)\]
Now, by multiplying the terms in the expression, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 1000000000 - 6000000 + 12000 - 8\]
Now, by simplifying the expression using the BODMAS rule, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 1000012000 - 6000008\]
Subtracting the terms, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 994011992\]
\[ \Rightarrow {\left( {998} \right)^3} = 994011992\]
Therefore, the value of \[{\left( {998} \right)^3}\]is \[994011992\].
Note:
We know that a binomial expression is defined as an algebraic expression having two terms and these terms must be unlike. We know that an equality relation which is true for all the values of the variables is called an Algebraic Identity. Here, we have used BODMAS rule which states that the first operation has to be done which is in the brackets, next the operation applies on the indices or order, then it moves on to the division and multiplication and then using addition and subtraction we will simplify the expression. If addition or subtraction and division or multiplication is in the same calculations, then it has to be done from left to right.
Formula used:
The cube of the difference of two numbers is given by an algebraic identity \[{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\].
Complete Step by Step Solution:
We are given an arithmetic expression \[{\left( {998} \right)^3}\].
Now, we will rewrite the given expression, which will be in the form of an Algebraic Identity, we get
\[{\left( {998} \right)^3} = {\left( {1000 - 2} \right)^3}\]
Thus, the expanded algebraic expression is in the form of an algebraic identity as \[{\left( {a - b} \right)^3}\] .
Now, by using an algebraic identity \[{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\], we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = {\left( {1000} \right)^3} - 3{\left( {1000} \right)^2}\left( 2 \right) + 3\left( {1000} \right){\left( 2 \right)^2} - {\left( 2 \right)^3}\]
Applying the exponent on the terms, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 1000000000 - 3\left( {1000000} \right)\left( 2 \right) + 3\left( {1000} \right)\left( 4 \right) - \left( 8 \right)\]
Now, by multiplying the terms in the expression, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 1000000000 - 6000000 + 12000 - 8\]
Now, by simplifying the expression using the BODMAS rule, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 1000012000 - 6000008\]
Subtracting the terms, we get
\[ \Rightarrow {\left( {1000 - 2} \right)^3} = 994011992\]
\[ \Rightarrow {\left( {998} \right)^3} = 994011992\]
Therefore, the value of \[{\left( {998} \right)^3}\]is \[994011992\].
Note:
We know that a binomial expression is defined as an algebraic expression having two terms and these terms must be unlike. We know that an equality relation which is true for all the values of the variables is called an Algebraic Identity. Here, we have used BODMAS rule which states that the first operation has to be done which is in the brackets, next the operation applies on the indices or order, then it moves on to the division and multiplication and then using addition and subtraction we will simplify the expression. If addition or subtraction and division or multiplication is in the same calculations, then it has to be done from left to right.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE