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Last updated date: 20th Jun 2024
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Answer
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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.