Homework Help

Remove the brackets and simplify: 2p(1+p+r)-3p(p-r-2)

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kavthuv | Student, Grade 9 | Valedictorian

Posted March 15, 2012 at 11:37 PM via web

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Remove the brackets and simplify:

2p(1+p+r)-3p(p-r-2)

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kavthuv | Student , Grade 9 | Valedictorian

Posted March 15, 2012 at 11:49 PM (Answer #1)

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thankyou

Top Answer

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted March 15, 2012 at 11:46 PM (Answer #2)

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You need to multiply each term of the sum `1+p+r`  by `2p`  and you need to multiply each term of the sum `p-r-2`  by `3p`  such that:

`2p(1 + p + r) = 2p*1 + 2p*p + 2p*r`

`2p(1 + p + r) = 2p + 2p^2 + 2pr`

`3p(p - r - 2) = 3p^2 - 3pr - 6p`

You need to subtract `3p^2 - 3pr - 6p`  from `2p + 2p^2 + 2pr`  such that:

`2p + 2p^2 + 2pr - (3p^2 - 3pr - 6p) = 2p + 2p^2 + 2pr - 3p^2+ 3pr+ 6p`

Collecting like terms yields:

`(2p^2 - 3p^2) + (2p + 6p) + (2pr + 3pr) = -p^2 + 8p + 5pr`

Hence,performing the simplification yields `2p(1 + p + r) - 3p(p - r - 2) = -p^2 + 8p + 5pr.`

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