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How can i factor this? 49-x^2-6xy-9y^2 i tried to group them in different ways but i...

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chipal08 | Student, Undergraduate | eNoter

Posted November 18, 2012 at 7:28 PM via web

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How can i factor this? 49-x^2-6xy-9y^2 

i tried to group them in different ways but i still can't get the answer which is -(x+3y+7)(x+3y-7) i think i've done something wrong but can't find out what it is so if anyone can please help coz i've been stuck in this problem for 25 minutes and i still have to do 12 problems thank you :D

 

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted November 19, 2012 at 2:20 AM (Answer #1)

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Factor `49-x^2-6xy-9y^2` :

Write as `49-(x^2+6xy+9y^2)`

The terms in the parantheses form a perfect square trinomial.

`=49-[(x+3y)^2]` But this is the difference of two squares:

`(7+(x+3y))(7-(x+3y))`

`=(7+x+3y)(7-x-3y)` Factoring a (-1) out of the second factor gets the answer in the form you were seeking:

`=-1(x+3y+7)(x+3y-7)`

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