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

Question 36 Factorization of Polynomials Exercise 3F

(𝑥 + 2)^3 − (𝑥 − 2)^3

Answer:

(𝑥 + 2)^3 − (𝑥 − 2)^3

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

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

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

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

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

= 4(3𝑥^2 + 4)

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