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

Question 33 Factorization of Polynomials Exercise 3F

(2𝑎 + 1)^3 + (𝑎 − 1)^3

Answer:

(2𝑎 + 1)^3 + (𝑎 − 1)^3

According to the equation

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

We get,

= ((2𝑎 + 1) + (𝑎 − 1))((2𝑎 + 1)^2 − (2𝑎 + 1)(𝑎 − 1) + (𝑎 − 1)^2)

According to the equation,

(𝑎 + 𝑏)^2 = 𝑎^2 + 2𝑎𝑏 + 𝑏^2

(𝑎 − 𝑏)^2 = 𝑎^2 − 2𝑎𝑏 + 𝑏^2

So we get,

= (2𝑎 + 1 + 𝑎 − 1)( (2𝑎)^2 + 2(2𝑎)(1) + 1^2 − 2𝑎^2 + 2𝑎 − 𝑎 + 1 + 𝑎^2 − 2𝑎(1) + 1^2)

= 3𝑎(4𝑎^2 + 4𝑎 + 1 − 2𝑎^2 + 𝑎 + 1 + 𝑎^2 − 2𝑎 + 1)

= 3𝑎(3𝑎^2 + 3𝑎 + 3)

By taking 3 as common

= 9𝑎(𝑎^2 + 𝑎 + 1)

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