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

Question 25 Factorization of Polynomials Exercise 3F

𝑎^3 + 3𝑎^2𝑏 + 3𝑎𝑏^2 + 𝑏^3 − 8

Answer:

𝑎^3 + 3𝑎^2𝑏 + 3𝑎𝑏^2 + 𝑏^3 − 8

We can write the given question as,

𝑎^3 + 3𝑎^2𝑏 + 3𝑎𝑏^2 + 𝑏^3 − 8 = (𝑎 + 𝑏)^3 − 2^3

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

(𝑎 + 𝑏)^3 − 2^3

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

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

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