Answer
Verified
417.9k+ views
Hint: Here in this question we have to simplify the given algebraic equation. To simplify the above algebraic equation we use arithmetic operation multiplication. It is also simplified by using the standard algebraic formula \[{(a - b)^2} = {a^2} - 2ab + {b^2}\]. Hence we can obtain the solution for the question.
Complete step-by-step solution:
The algebraic expression or equation is a combination of variables, constants and arithmetic operations.
The equation can be simplified by using two methods.
Method 1:
Now consider the given equation \[{(x - 2y)^2}\]
The exponential form can be expanded
\[ \Rightarrow (x - 2y)(x - 2y)\]
The terms in the braces are multiplied. On multiplying we get
\[ \Rightarrow x(x - 2y) - 2y(x - 2y)\]
On term-by-term multiplication
\[ \Rightarrow {x^2} - 2xy - 2xy + 4{y^2}\]
On simplifying we get
\[{x^2} - 4xy + 4{y^2}\]
Hence we have simplified the given equation
Method 2:
We solve or simplify the given algebraic equation by using the standard algebraic formula \[{(a - b)^2} = {a^2} - 2ab + {b^2}\].
Now consider the given equation \[{(x - 2y)^2}\]. On comparing the standard algebraic formula and the given equation. The value of a is x and the value of b is 2y.
On substituting these values in the algebraic formula we get
\[ \Rightarrow {(x - 2y)^2} = {(x)^2} - 2(x)(2y) + {(2y)^2}\]
On squaring and simplifying the terms we get
\[ \Rightarrow {(x - 2y)^2} = {x^2} - 4xy + 4{y^2}\]
Hence we have simplified the given equation
Solving the equation by method 1 and method 2 we have obtained the final answer as the same.
Therefore \[{(x - 2y)^2} = {x^2} - 4xy + 4{y^2}\]
Note: To multiply we use operation multiplication, multiplication of numbers is different from the multiplication of algebraic expression. In the algebraic expression it involves the both number that is constant and variables. Variables are also multiplied, if the variable is the same then the result will be in the form of exponent. We must know about the standard algebraic formulas.
Complete step-by-step solution:
The algebraic expression or equation is a combination of variables, constants and arithmetic operations.
The equation can be simplified by using two methods.
Method 1:
Now consider the given equation \[{(x - 2y)^2}\]
The exponential form can be expanded
\[ \Rightarrow (x - 2y)(x - 2y)\]
The terms in the braces are multiplied. On multiplying we get
\[ \Rightarrow x(x - 2y) - 2y(x - 2y)\]
On term-by-term multiplication
\[ \Rightarrow {x^2} - 2xy - 2xy + 4{y^2}\]
On simplifying we get
\[{x^2} - 4xy + 4{y^2}\]
Hence we have simplified the given equation
Method 2:
We solve or simplify the given algebraic equation by using the standard algebraic formula \[{(a - b)^2} = {a^2} - 2ab + {b^2}\].
Now consider the given equation \[{(x - 2y)^2}\]. On comparing the standard algebraic formula and the given equation. The value of a is x and the value of b is 2y.
On substituting these values in the algebraic formula we get
\[ \Rightarrow {(x - 2y)^2} = {(x)^2} - 2(x)(2y) + {(2y)^2}\]
On squaring and simplifying the terms we get
\[ \Rightarrow {(x - 2y)^2} = {x^2} - 4xy + 4{y^2}\]
Hence we have simplified the given equation
Solving the equation by method 1 and method 2 we have obtained the final answer as the same.
Therefore \[{(x - 2y)^2} = {x^2} - 4xy + 4{y^2}\]
Note: To multiply we use operation multiplication, multiplication of numbers is different from the multiplication of algebraic expression. In the algebraic expression it involves the both number that is constant and variables. Variables are also multiplied, if the variable is the same then the result will be in the form of exponent. We must know about the standard algebraic formulas.
Recently Updated Pages
Who among the following was the religious guru of class 7 social science CBSE
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Trending doubts
Derive an expression for drift velocity of free electrons class 12 physics CBSE
Which are the Top 10 Largest Countries of the World?
Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
The energy of a charged conductor is given by the expression class 12 physics CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Derive an expression for electric field intensity due class 12 physics CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Derive an expression for electric potential at point class 12 physics CBSE