Question

Find the volume:V=x(3x+1)(x-5)

Answer 1

`3x^(3) - 14x^(2) - 5x`

Explanation:

I'm assuming what you're looking for is the expansion, or simplification, of the right side of that equation: x(3x + 1)(x - 5). So, let's go ahead and do that; let me know if you're looking for something else.

First, let's distribute that "x" at the beginning of the expression onto that first parenthetical expression, (3x + 1).

`x(3x + 1) = x(3x) + x(x) = 3x^(2) + x`

Now we have something different to simplify,
`(3x^(2) + x)(x - 5)`.

`(3x^(2) + x)(x - 5) = \\3x^(2)(x) + 3x^(2)(-5) + x(x) + x(-5) = \\3x^(3) - 15x^(2) + x^(2) - 5x = \\3x^(3) - 14x^(2) - 5x`

And there's our answer. Hopefully that was helpful - again, if you have any more questions, please let me know. :)