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

Question 38 Factorization of Polynomials Exercise 3F

(59×59×59−9×9×9)/(59×59+59×9+9×9)= 50

Answer:

(59×59×59−9×9×9)/(59×59+59×9+9×9)= 50

Let us take 59 = a and 9 = b

So we know that LHS

= So we know that LHS

=(𝑎×𝑎×𝑎−𝑏×𝑏×𝑏)/(𝑎×𝑎+𝑎×𝑏+𝑏×𝑏)

=(𝑎^3+𝑏^3)/(𝑎^2+𝑎𝑏+𝑏^2)

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

=[(𝑎−𝑏)(𝑎^2+𝑎𝑏+𝑏^2)]/(𝑎^2+𝑎𝑏+𝑏^2)

Since (𝑎^2 + 𝑎𝑏 + 𝑏^2) is similar in numerator and denominator

We get,

= (a – b)

Now by replacing the values of a and b

= 59 – 9

= 50

= RHS

Hence proved.

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