Find the expansion of
$(p + 2) (p - 4) (p + 6)$

p^{3} + 4 p^{2} - 20 p - 48

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p^{3} - 4 p^{2} - 20 p - 48

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p^{3} + 4 p^{2} + 20 p - 48

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None of these

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Solution

The correct option is B $p^{3} + 4 p^{2} - 20 p - 48$
We solve the given expression $(p + 2) (p - 4) (p + 6)$ as shown below:

$[(p + 2) (p - 4)] (p + 6)$

$= [p (p - 4) + 2 (p - 4)] (p + 6)$

$= (p^{2} - 4 p + 2 p - 8) (p + 6)$

$= (p^{2} - 2 p - 8) (p + 6) (C o m b i n i n g l i k e t e r m s)$

$= (p + 6) (p^{2} - 2 p - 8)$

$= p (p^{2} - 2 p - 8) + 6 (p^{2} - 2 p - 8)$

$= p^{3} - 2 p^{2} - 8 p + 6 p^{2} - 12 p - 48$

$= p^{3} + (6 - 2) p^{2} + (- 8 - 12) p - 48 (C o m b i n i n g l i k e t e r m s)$

$= p^{3} + 4 p^{2} - 20 p - 48$

Hence, $(p + 2) (p - 4) (p + 6) = p^{3} + 4 p^{2} - 20 p - 48$

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