Question #600cc

2 Answers
Feb 13, 2018

(x-5)(x-5)(x-5)=x^3-15x^2+75x-125

Explanation:

First, Let's Use the formula

(a-b)(a-b)(a-b)=(a-b)^3=a^3-3ba^2+3ab^2-b^3

Then,Subsutite a=x and b=5,so

(x-5)^3=x^3-(3)(5)x^2+3(x)(5^2)-5^3
=x^3-15x^2+75x-125

Feb 13, 2018

x^3-15x^2+75x-125

Explanation:

Start by expanding the first two terms. You may have learned the FOIL method, where you multiply First, Outer, Inner, then Last terms. Here it is with the first two:
(x-5)(x-5)
First: x*x = x^2
Outer: x*-5 = -5x
Inner: -5*x = -5x
Last: -5*-5 = 25

Now add the like terms together.
x^2 -5x-5x+25
x^2-10x+25

Now multiply that trinomial by the final binomial:
x^2*x = x^3
x^2*-5 = -5x^2
-10x*x = -10x^2
-10x*-5 = 50x
25*x = 25x
25*-5 = -125

Again, add all like terms together to get your final answer.
x^3-5x^2-10x^2+50x+25x-125

x^3-15x^2+75x-125