Question

Question #600cc

Answer 1

`(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`

Answer 2

`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`