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

Question 35 Factorization of Polynomials Exercise 3F

(𝑥 + 2)^3 + (𝑥 − 2)^3


(𝑥 + 2)^3 + (𝑥 − 2)^3

According to the equation

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

We get,

= ((𝑥 + 2) + (𝑥 − 2))((𝑥 + 2)^2 − (𝑥 + 2)(𝑥 − 2) + (𝑥 − 2)^2)

According to the equation,

(𝑎 + 𝑏)^2 = 𝑎^2 + 2𝑎𝑏 + 𝑏^2

(𝑎 − 𝑏)^2 = 𝑎^2 − 2𝑎𝑏 + 𝑏^2

So we get,

= (𝑥 + 2 + 𝑥 − 2)( 𝑥^2 + 2(𝑥)(2) + (2)^2 − (𝑥^2 − 2^2) + 𝑥^2 − 2(𝑥)(2) + 2^2)

= 2𝑥(𝑥^2 + 4𝑥 + 4 − 𝑥^2 + 4 + 𝑥^2 − 4𝑥 + 4)

= 2𝑥(𝑥^2 + 12)

Video transcript
"hi students welcome to redo learning here i am your leader tutor to help you solve the question the question we have is x plus 2 whole q plus x minus 2 whole q now here we will consider x plus 2 as a aq and x minus 2 as a b cube now here we'll apply the formula a plus b in bracket a square minus a b plus b square so we'll write this x plus 2 plus x minus 2. in the second bracket x plus 2 whole square minus x plus 2 multiplied by x minus 2 plus x minus 2 whole square now if you simplify the first part this minus 2 minus will get cancelled and the answer will be 2 x in the second bracket the big bracket first will write the x plus 2 whole square x square plus 4 x plus 4 minus now if we simplify this to bracket x plus 2 x minus 2 we can write it as a x square a square minus b square so x square minus b square which is equals to 4. in the third bracket x square minus 4x plus 4. now we'll simplify the square brackets now for the square bracket we can write we can see it's x square x square x square will get added so it will be 2 x square plus 4 x and minus 4 x will get cancelled then 4x and 4x will further get added so it's 8 minus x square plus 4. this is in the bracket part now if we simplify the bracket further this 8 plus 4 will be 12 and 2x square minus x square will be x square so it's x square plus 12 so x square plus 12 in bracket in outside the bracket it's 2x now the answer will be 2 x cube plus 24. so this is the simplified answer that we get for this question which is 2 x cube plus 24. so what we did we first applied the aq plus bq formula the next we applied in the bracket it's a square a plus b whole square and here the bracket a square minus b square here a minus b whole square on further simplification of the bracket we can see we are getting x square plus 12 and an outside the bracket we are getting 2x so this way further simplification give us the answer 2x cube plus 24. so i hope you understood the question for any doubt you can write in the comment section for regular updates do subscribe to the video channel thank you "
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