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

Answer 1

Eva Abramson

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

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

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

It could be beneficial to mention that as well:

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

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

Thus, upon distribution, we obtain:

#-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#

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Answer 2

Jameson Allen

To multiply (-p^2(p-11)), you would distribute (-p^2) to both terms inside the parentheses. This results in (-p^3 + 11p^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.