How do you multiply #-p^2 (p-11)#?

1 Answer
Jul 1, 2015

Answer:

Use the distributive property (also known as the distributive law or rule).

Explanation:

The distributive property says that for any numbers #a, b, "and " c#, we have:

#a(b+c) = a*b+b*c#

It may help to also point out that:

#p# may be thought of as #1p# and
#-p^2# is #-1p^2#.

Finally, #p-11# is the same as #p + (-11)#

So when we distribute, we get:

#-p^2(p-11) = -p^2(p+(-11))#

# = -p^2*p +(-p^2)(-11)#

# = -p^3 +(11p^2)#

# = -p^3+11p#

With experience, it becomes quicker to see that "when we distribute a minus sign, we have to change the signs" so, for example:
#-2(4x-7) = -8x+14#
and
#-3(-5x-9) = 15x+27#
and
#-x(-x+4) = x^2-4x#