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expand x^3+y^3

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user4825270 | Student | eNoter

Posted August 2, 2013 at 9:23 PM via web

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expand x^3+y^3

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llltkl | College Teacher | Valedictorian

Posted August 3, 2013 at 1:50 AM (Answer #1)

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

So,` x^3+y^3=(x+y)^3-3x^2y-3xy^2`

                   `=(x+y)^3-3xy(x+y)`

                   `=(x+y){(x+y)^2-3xy}`

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

                   `=(x+y)(x^2-xy+y^2)`

Therefore, `x^3+y^3=(x+y)(x^2-xy+y^2)`

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