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

Question 24 Factorization of Polynomials Exercise 3F

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

Answer:

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

= (2𝑎)^3 − 𝑏^3 − 2𝑥(2𝑎 − 𝑏)

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

On further simplification

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2) − 2𝑥(2𝑎 − 𝑏)

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2 − 2𝑥)

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