SOLUTION: Need help with this (x-1)(x^3+x^2+x)=? Thank you

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Question 329605: Need help with this (x-1)(x^3+x^2+x)=? Thank you
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
(x-1)(x^3+x^2+x) = ?

Use the distributive law of multiplication to get:

(x-1)(x^3+x^2+x) equals:

(x * (x^3+x^2+x)) - (1 * (x^3+x^2+x))

This becomes:

x^4 + x^3 + x^2 - x^3 - x^2 - x

Combine like terms to get:

x^4 - x

That's your answer.

You can confirm by taking any value of x and showing that the original form of the equation and the final form of the equation give you the same answer.

Let x = 3

(x-1) * (x^3 + x^2 + x) becomes:
2 * (27 + 9 + 3) which becomes:
2 * 39 which becomes:
78

x^4 - x becomes:
81 - 3 which becomes:
78

Since the original form of the equation and the final form of the equation give you the same answer, then you should be good.

If you graph both equations, they should be identical.

A graph of the original equation looks like this:

graph%28600%2C400%2C-5%2C5%2C-10%2C100%2C%28x-1%29%2A%28x%5E3%2Bx%5E2%2Bx%29%29

A graph of the final equation looks like this:

graph%28600%2C400%2C-5%2C5%2C-10%2C100%2C100%2Cx%5E4+-+x%29%29

a graph of both equations superimposed on each other looks like this:


graph%28600%2C400%2C-5%2C5%2C-10%2C100%2C%28x-1%29%2A%28x%5E3%2Bx%5E2%2Bx%29%2Cx%5E4+-+x%29