Question

Find the expansion of

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

• A. $p^3+4p^2+20p-48$
• B. $p^3+4p^2-20p-48$
• C. $p^3-4p^2-20p-48$
• D. None of these

Answer 1

Answer: (B)

We solve the given expression $(p+2)(p-4)(p+6)$ as shown below:

$\left[\right(p+2\left)\right(p-4\left)\right](p+6)$

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

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

$=(p^2-2p-8)(p+6)\left(Combiningliketerms\right)$

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

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

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

$=p^3+(6-2)p^2+(-8-12)p-48\left(Combiningliketerms\right)$

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

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