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Question
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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