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10(3𝑥 +1/𝑥)^2 − (3𝑥 +1/𝑥) − 3

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10(3𝑥 +1/𝑥)^2 − (3𝑥 +1/𝑥) − 3

Consider,

3𝑥 +1/𝑥= a

So we get,

= 10𝑎^2 − 𝑎 − 3

We can further write it as

= 10𝑎^2 − 6𝑎 + 5𝑎 − 3

By taking out the common terms

= 2a (5a – 3) + 1 (5a – 3)

= (2a + 1) (5a – 3)

Let us replace a by 3𝑥 +1/𝑥

So we get,

(2(3𝑥 +1/𝑥) + 1) (5(3𝑥 +1/𝑥) – 3)

On further multiplication,

= (6x +2/𝑥+ 1) (15x +5/𝑥– 3)

"hello everyone i am sumanjali math tutor from leader learning welcome to question and answer session given expression is 10 into 3x plus 1 by x whole square minus 3x plus 1 by x minus 3 this is the expression and we need to factorize this expression factorization is nothing but we need to express this in terms of simple terms that are factors for this expression as the expression is a bit complicated with these terms 3x plus 1 by x so we can write so let us take let us take an another value in place of 3x plus 1 by x okay so the value will be a okay i am taking the value as a okay so this is 10 a square the expression can be rewrite as 10 a square minus a minus 3 okay this is the expression and we need to find the factors for this expression as the expression is in the form of a x square plus b x plus c okay to factorize this we need to take the product of a and c first where a is the coefficient of x square that is the value will be 10 and c will be constant the value will be three okay then threes are 30 and we need to find an another set of factors for this 30 that are six five because if we add or subtract we should get the value of b that is one okay b is the coefficient of x that is one so i can simply get like yeah so i can get it from 6 minus 5 so i will get minus 1 minus 1 x from minus 1 x as minus 6 x plus 5 x or i can write this as 5x minus 6x also okay so or 5a minus 6a actually it is in the terms of a so i can write minus 5a minus 6a okay so this is 10 a square 10 a square plus 5 a minus 6 a minus 3 so i'm taking 5a common from the first two terms 5 twos are 10 so 2 a will remains plus 1 will be there okay so here i am taking minus 3 common so that here 2 a will be there plus 1 if i take a common 2 a plus 1 5 a minus 3 will be remains here okay so the expression 10 a square minus a plus 3 can be written as 2 a plus 1 into 5 a minus 3 5 a minus 3 and the expression 10 into 3x plus 1 by x whole square minus 3x plus 1 by x minus 3 can be expressed as 2 into in place of a i'm writing 3x plus 1 by x plus 1 into 5 a that is 5 into 3x plus 1 by x minus 3 okay so this is the expression so that's all hope you understand if you have further questions reach us at comment section and subscribe to the channel leader learning for further queries thank you"

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