Question

Hey can someone help I don't really understand this 3 (x^3-2)?

Answer 1

`3(x^3-2)=color(blue)(3x^3-6)`

Explanation:

Note that by the distributive property, for any values `color(magenta)a` and `color(lime)b`
`color(white)("XXX")3(color(magenta)a+color(lime)b)=3 * color(magenta)a+3 * color(lime)b`

In this case `color(magenta)a=color(magenta)(x^3)`
`color(white)("XXXX")`and `color(lime)b=color(lime)(""(-2))`

So
`color(white)("XXX")3(color(magenta)(x^3)color(lime)(-2))`

`color(white)("XXXXXX")=3 * color(magenta)(x^3) + 3 * color(lime)(""(-2))`

`color(white)("XXXXXX")=3x^3color(white)("xx")-6`

Answer 2

The expanded expression is `3x^3-6`.

Explanation:

To expand this expression, we use something called the distributive property. Basically, it says this:

`color(red)a*(color(blue)b+color(green)c)qquad=qquadcolor(red)a*color(blue)bquad+quadcolor(red)a*color(green)c`

When you multiply two things in parentheses, you can distribute the multiplying term onto each of the terms in the parentheses.

Now, here's our expression. We can use the distribute property to distribute the `3` onto each of the terms. It will look like this:

`color(white)=3 (x^3-2)`

`=color(red)3 (color(blue)(x^3)-color(green)2)`

`=color(red)3*color(blue)(x^3)quad-quadcolor(red)3*color(green)2`

`=color(purple)(3x^3)quad-quadcolor(red)3*color(green)2`

`=color(purple)(3x^3)quad-quadcolor(brown)6`

That's how you use the distributive property. Hope this helped!