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Factorization of Polynomials | Factorization of Polynomials Exercise 3F

Question 17

3𝑎^7𝑏 − 81𝑎^4𝑏^4

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  • Solution

  • Transcript

3𝑎^7𝑏 − 81𝑎^4𝑏^4

We can write the given question as,

3𝑎^7𝑏 − 81𝑎^4𝑏^4 = 3𝑎^4𝑏(𝑎^3 − 27𝑏^3)

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

3𝑎^4𝑏(𝑎^3 − 27𝑏^3)

= 3𝑎^4𝑏(𝑎^3 − (3𝑏)^3)

Using the equation,

= 3𝑎^4𝑏[(𝑎 − 3𝑏)(𝑎^2 + 𝑎(3𝑏) + (3𝑏)^2)]

= 3𝑎^4𝑏(𝑎 − 3𝑏)(𝑎^2 + 3𝑎𝑏 + 9𝑏^2)

"hello guys welcome back to leader homework i'm revan kumar working as a tutor that leader so today we are going to solve one more very interesting and easiest problem so let's see how we can do it and how we can solve it okay so now they have given here the question it has 3 a power 7 b minus 81 a power 4 b power 4 right so by this question we cannot do anything directly so if you are taking anything common we can do it right so if you are taking the common thing as uh that is 3 a power a power 4 b okay if you are taking 3 a po 4 b as common you will be remaining left over with here a q minus 27 uh they are you have taken like a cube if you are taking a 4 common a cube will be there and here you will be left over with your b cube right so that is only the thing so 3 a power 4 b you have to common here then this will be left over inside it right so this will be exactly you can write it in the format of a cube minus 3 b whole cube right so again it is in the format of what a cube minus b cube so that is equals to a minus b of a square plus a b plus b square right so that is just substitute each and everything here so this is a and this is b here so after substituting each you will be getting a minus three be off a minus three be off there a square means a square only place a into three b plus 3 b whole square so that you will be getting the answer as a minus 3 b of a square plus 3 a b plus 9 b square so that is our final answer here i hope you understand what i've done so before that there we have took this common no so we'll be writing here 3 a power 4 b so i hope you understand what i've done here if you have any doubts please comment below don't forget to subscribe to this channel thank you so much for watching this please subscribe to this channel for further updates thank you "

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Question 17

3𝑎^7𝑏 − 81𝑎^4𝑏^4

  • Solution

  • Transcript

3𝑎^7𝑏 − 81𝑎^4𝑏^4

We can write the given question as,

3𝑎^7𝑏 − 81𝑎^4𝑏^4 = 3𝑎^4𝑏(𝑎^3 − 27𝑏^3)

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

3𝑎^4𝑏(𝑎^3 − 27𝑏^3)

= 3𝑎^4𝑏(𝑎^3 − (3𝑏)^3)

Using the equation,

= 3𝑎^4𝑏[(𝑎 − 3𝑏)(𝑎^2 + 𝑎(3𝑏) + (3𝑏)^2)]

= 3𝑎^4𝑏(𝑎 − 3𝑏)(𝑎^2 + 3𝑎𝑏 + 9𝑏^2)

"hello guys welcome back to leader homework i'm revan kumar working as a tutor that leader so today we are going to solve one more very interesting and easiest problem so let's see how we can do it and how we can solve it okay so now they have given here the question it has 3 a power 7 b minus 81 a power 4 b power 4 right so by this question we cannot do anything directly so if you are taking anything common we can do it right so if you are taking the common thing as uh that is 3 a power a power 4 b okay if you are taking 3 a po 4 b as common you will be remaining left over with here a q minus 27 uh they are you have taken like a cube if you are taking a 4 common a cube will be there and here you will be left over with your b cube right so that is only the thing so 3 a power 4 b you have to common here then this will be left over inside it right so this will be exactly you can write it in the format of a cube minus 3 b whole cube right so again it is in the format of what a cube minus b cube so that is equals to a minus b of a square plus a b plus b square right so that is just substitute each and everything here so this is a and this is b here so after substituting each you will be getting a minus three be off a minus three be off there a square means a square only place a into three b plus 3 b whole square so that you will be getting the answer as a minus 3 b of a square plus 3 a b plus 9 b square so that is our final answer here i hope you understand what i've done so before that there we have took this common no so we'll be writing here 3 a power 4 b so i hope you understand what i've done here if you have any doubts please comment below don't forget to subscribe to this channel thank you so much for watching this please subscribe to this channel for further updates thank you "

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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