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RS Aggarwal Solutions Class 9 Mathematics Solutions for Factorization of Polynomials Exercise 3F in Chapter 3 - Factorization of Polynomials

Question 23 Factorization of Polynomials Exercise 3F

(𝑎 + 𝑏)^3 − (𝑎 − 𝑏)^3

Answer:

(𝑎 + 𝑏)^3 − (𝑎 − 𝑏)^3

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

(𝑎 + 𝑏)^3 − (𝑎 − 𝑏)^3

= (𝑎 + 𝑏 − (𝑎 − 𝑏))((𝑎 + 𝑏)^2 + (𝑎 + 𝑏)(𝑎 − 𝑏) + (𝑎 − 𝑏)^2)

On further simplification

= (𝑎 + 𝑏 − 𝑎 + 𝑏)(𝑎^2 + 𝑏^2 + 2𝑎𝑏 + 𝑎^2 − 𝑏^2 + 𝑎^2 + 𝑏^2 − 2𝑎𝑏)

= 2𝑏(3𝑎^2 + 𝑏^2)

Video transcript
"hello guys welcome back to the room work i'm revant kumar working as a tutorial so today we are going to solve and explore one very easy question and it will be very easy to solve also so let's see how we can do it okay so the question i have given here it has a plus b whole cube minus a minus b whole cube oh my god a plus b whole cube minus minus b whole cube we cannot do it like very easily so we can do it very easily also that is it is in the format of aq minus b cube right so a q minus b cube so this is a and this is b yo so that is a minus b of a square plus a b plus b square u so we can do it here a minus b that is a plus b minus a minus b right so of a square that is a plus b whole square plus a b that means a plus b of a minus b and again plus b square that is a minus b whole square here so now it will be very interesting so a plus a plus b and your minus a plus b right so a minus a plus b minus a plus a will be getting canceled and 2 b of a plus b whole square that is a square plus b square plus 2 a b and here plus a plus b of minus b means a square minus b square and here plus again a square plus b square minus 2 a b right because it is m s b o square know minus 2 a b b and here plus 2 a b will be getting cancel and plus b square minus b square also will be getting cancelled and it will be remained with to be off so i'm writing with another color so 2b of a square a square plus a square here a square plus a square and plus a square here again and plus b square right so this is our final answer and 2 b of 3 squared plus b square so i hope you have understood like what i've done here if you have any doubts please comment below don't forget to subscribe to the channel thank you so much for watching this stay tuned thank you "
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