Answer
Verified
421.8k+ views
Hint: We are given an equation and we have to find its factor. For this we can begin by setting the equation equal to zero. Then we will take the factor out of the equation. Then after the equation is formed then apply the algebraic identity. Here according to the equation we will apply the identity. Identity which involves the difference of the squares of two numbers.
Formula used:
$A^2-B^2$= (A-B) (A+B)
Complete step-by-step answer:
Step1: We are given an equation $6{x^2} = 600$ first we will set the equation equal to zero.
$ \Rightarrow 6{x^2} = 600$
$6{x^2} - 600 = 0$
Then we will factor out $6$ as $6$ is common in both the terms.
$ \Rightarrow 6\left( {{x^2} - 100} \right)$
Step2: Now if we recognize that $\left( {{x^2} - 100} \right)$ is the difference of two squares as ${x^2}$ is the square of $x$ and $100$ is $10$.$x \times x$ And $10 \times 10$ with signs + or – between them we will apply the algebraic identities for ${x^2} - 100$.
Using the identity:
$A^2-B^2$= (A-B) (A+B)
Here ${A^2} = {x^2};{B^2} = 100$
$ \Rightarrow \left( {{x^2} - 100} \right) = (x - 10)(x + 10)$
So the factors will be $6\left( {x - 10} \right)\left( {x + 10} \right)$
Hence the factors are $6\left( {x - 10} \right)\left( {x + 10} \right)$.
Note:
In such types of questions students mainly don't get an approach how to solve it. In such types of algebraic expressions mainly and first equate them to zero then the algebraic identity gets applied which factorize the whole expression. Sometimes we have to factor out a number from an expression then the expression forms in a way so that it can be factorized and identity can be applied. There are many algebraic identities apart from this which we have used in this question we have to just apply the identity correctly. Many times students forget the identity as there are many identities so they mix match them and apply them wrong. So before solving such questions revise the identities so the chances of getting questions wrong becomes very less. The main approach to solve these questions is to form a question in such a way and then apply identity.
Formula used:
$A^2-B^2$= (A-B) (A+B)
Complete step-by-step answer:
Step1: We are given an equation $6{x^2} = 600$ first we will set the equation equal to zero.
$ \Rightarrow 6{x^2} = 600$
$6{x^2} - 600 = 0$
Then we will factor out $6$ as $6$ is common in both the terms.
$ \Rightarrow 6\left( {{x^2} - 100} \right)$
Step2: Now if we recognize that $\left( {{x^2} - 100} \right)$ is the difference of two squares as ${x^2}$ is the square of $x$ and $100$ is $10$.$x \times x$ And $10 \times 10$ with signs + or – between them we will apply the algebraic identities for ${x^2} - 100$.
Using the identity:
$A^2-B^2$= (A-B) (A+B)
Here ${A^2} = {x^2};{B^2} = 100$
$ \Rightarrow \left( {{x^2} - 100} \right) = (x - 10)(x + 10)$
So the factors will be $6\left( {x - 10} \right)\left( {x + 10} \right)$
Hence the factors are $6\left( {x - 10} \right)\left( {x + 10} \right)$.
Note:
In such types of questions students mainly don't get an approach how to solve it. In such types of algebraic expressions mainly and first equate them to zero then the algebraic identity gets applied which factorize the whole expression. Sometimes we have to factor out a number from an expression then the expression forms in a way so that it can be factorized and identity can be applied. There are many algebraic identities apart from this which we have used in this question we have to just apply the identity correctly. Many times students forget the identity as there are many identities so they mix match them and apply them wrong. So before solving such questions revise the identities so the chances of getting questions wrong becomes very less. The main approach to solve these questions is to form a question in such a way and then apply identity.
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