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

Question 18 Factorization of Polynomials Exercise 3F

𝑥^4𝑦^4 − 𝑥𝑦

Answer:

𝑥^4𝑦^4 − 𝑥𝑦

We can write the given question as,

𝑥^4𝑦^4 − 𝑥𝑦 = 𝑥𝑦(𝑥^3𝑦^3 − 1)

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

𝑥𝑦(𝑥^3𝑦^3 − 1)

= 𝑥𝑦((𝑥𝑦)^3 − 1^3)

Using the equation,

= 𝑥𝑦[(𝑥𝑦 − 1)((𝑥𝑦)^2 + (𝑥𝑦)(1) + (1)^2)]

= 𝑥𝑦(𝑥𝑦 − 1)(𝑥^2𝑦^2 + 𝑥𝑦 + 1)]

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