Question

What is the standard form of `y= (x+2) (2x+5)`?

Answer 1

`y=2x^2+9x+10`

Explanation:

If we start with `y=(x+2)(2x+5)`, and we are trying to convert this into standard form, our first step is to expand this. Later on we'll combine like-terms and tidy up any stray pieces.

So, let's expand `(color(green)(x)+color(orange)(2))*(color(blue)(2x)+color(red)(5))`. `color(green)(x)` multipled by `color(blue)(2x)` is `2x^2` and `color(green)(x)` times `color(red)(5)` equals `5x`. `color(orange)(2)` times `color(blue)(2x)` is `4x`, and `color(orange)(2)` by `color(red)(5)` is `10`. That means we now have `2x^2+5x+4x+10`.

From there we just need to combine like-terms. `5x+4x` is `9x`. That's all we can combine. Let's take another look at the equation: `y=2x^2+9x+10`. That looks like it is in `ax^2+bx+c` format to me, don't 'ya think ;). I think our work is done. Nice job!