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

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### 2 Answers

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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