Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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Simplify x3-y33x2+9xy+6y2×x2+2xy+y2x2-y2 - Mathematics

Sum

Simplify `(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`

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Solution

x3 – y3 = (x – y) (x2 + xy + y2)

x2 + 2xy + y2 = (x + y) (x + y)


3x2 + 9xy + 6y2 = 3(x2 + 3xy + 2y2)

= 3 (x + 2y) (x + y)

(x2 – y2) = (x + y) (x – y)

`(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`

= `((x - y)(x^2 + xy + y^2))/(3(x + 2y)(x + y)) xx ((x + y)(x + y))/((x + y)(x - y))`

= `(x^2 + xy + y^2)/(3(x + 2y))`

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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 3 Algebra
Exercise 3.5 | Q 2. (ii) | Page 101
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