Question

I need someone to explain to me how to simplify (x^2+3)[3x+(8-x^2)]

Answer 1

\[\Large (x^2+3)\left[3x+\color{#FF0080}{(}8-x^2\color{#FF0080}{)}\right]\]
First of all, see how there is no operation (multiplication/division) being performed on the outside of these pink brackets? That tells us we can drop the brackets.\[\Large (x^2+3)\left[3x+8-x^2\right]\]So we need to multiply this out? :O oh boy

Answer 2

To expand this out, we take the `first term` in the `first brackets`,
and multiply it by `each term` in the `second brackets`. Adding successive terms.

So here is how we would start.\[\Large (\color{royalblue}{x^2}+3)\left[3x+8-x^2\right]\]We'll multiply this x^2 by each term in the second set of brackets, adding as we go along.\[\Large =\color{royalblue}{x^2}\cdot3x\quad+\quad\color{royalblue}{x^2}\cdot8\quad+\quad\color{royalblue}{x^2}\cdot(-x^2)\]

After we simplify by doing the multiplication, that takes care of the first 3 terms.
We need to also distribute the `3` to each term in the second set of brackets.

Answer 3

Is this process making sense? <:o