Answer
Verified
410.4k+ views
Hint: In this question we need to find the simplified form of \[{\left( {x - 3} \right)^3}\]. Here, \[\left( {x - 3} \right)\]being multiplied \[3\] times that is \[\left( {x - 3} \right)\left( {x - 3} \right)\left( {x - 3} \right)\], the output of it will yield an equation that has \[{x^3}\] as the variable with largest power, thus the equation will be cubic equation.
Complete step by step solution:
As we know that the equation of the form $a{x^3} + {x^2} + cx + d$ is known as the cubic equation. Here, $x$ is the variable, $a$, $b$, and $c$ are the coefficients and$d$ is the constant. The largest power of the variable in the equation is three and it determines that the equation is cubic.
In this question, we have given a term that is and we need to simplify it.
Here, is multiplied three times.
Here, we will consider the algebraic identity \[{\left( {a - b} \right)^3} = {a^3} - {b^3} - 3ab\left( {a + b} \right)\]
Now we will apply this algebraic identity to the given equation as,
\[ \Rightarrow {\left( {x - 3} \right)^3} = {x^3} - {3^3} - 3x\left( 3 \right)\left( {x + 3} \right)\]
Now, we will simplify the above expression as,
\[ \Rightarrow {\left( {x - 3} \right)^3} = {x^3} - 9 - 9x\left( {x + 3} \right)\]
Now, we will multiply $9x$ in the bracket terms as,
\[ \Rightarrow {\left( {x - 3} \right)^3} = {x^3} - 9 - 9{x^2} - 27x\]
After simplification we will get,
\[\therefore {\left( {x - 3} \right)^3} = {x^3} - 9{x^2} - 27x - 9\]
From above, the expanded form of the \[{\left( {x - 3} \right)^3} = {x^3} - 9{x^2} - 27x - 9\].
Note:
The exponent is the number of times a number can be multiplied by itself. For example consider a variable $a$ as $a \times a = {a^2}$ , then ${a^n}$ represents $a$ multiplied by itself n number of times. The exponent form${a^n}$ is pronounced as a raise to the power n. Where,
${a^0} = 1$ And${a^1} = a$. The other properties are${\left( {ab} \right)^n} = {a^n}{b^n}$, also ${a^n}{a^m} = {a^{m + n}}$.
Complete step by step solution:
As we know that the equation of the form $a{x^3} + {x^2} + cx + d$ is known as the cubic equation. Here, $x$ is the variable, $a$, $b$, and $c$ are the coefficients and$d$ is the constant. The largest power of the variable in the equation is three and it determines that the equation is cubic.
In this question, we have given a term that is and we need to simplify it.
Here, is multiplied three times.
Here, we will consider the algebraic identity \[{\left( {a - b} \right)^3} = {a^3} - {b^3} - 3ab\left( {a + b} \right)\]
Now we will apply this algebraic identity to the given equation as,
\[ \Rightarrow {\left( {x - 3} \right)^3} = {x^3} - {3^3} - 3x\left( 3 \right)\left( {x + 3} \right)\]
Now, we will simplify the above expression as,
\[ \Rightarrow {\left( {x - 3} \right)^3} = {x^3} - 9 - 9x\left( {x + 3} \right)\]
Now, we will multiply $9x$ in the bracket terms as,
\[ \Rightarrow {\left( {x - 3} \right)^3} = {x^3} - 9 - 9{x^2} - 27x\]
After simplification we will get,
\[\therefore {\left( {x - 3} \right)^3} = {x^3} - 9{x^2} - 27x - 9\]
From above, the expanded form of the \[{\left( {x - 3} \right)^3} = {x^3} - 9{x^2} - 27x - 9\].
Note:
The exponent is the number of times a number can be multiplied by itself. For example consider a variable $a$ as $a \times a = {a^2}$ , then ${a^n}$ represents $a$ multiplied by itself n number of times. The exponent form${a^n}$ is pronounced as a raise to the power n. Where,
${a^0} = 1$ And${a^1} = a$. The other properties are${\left( {ab} \right)^n} = {a^n}{b^n}$, also ${a^n}{a^m} = {a^{m + n}}$.
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