Question

What is the standard form of `y= 3(2x + 1)(x - 5)`?

Answer 1

`6x^2-27x-15`

Explanation:

`3color(blue)((2x+1)(x-5))`

Let's ignore the `3` for now. What I have in blue, we can multiply using the mnemonic FOIL (Firsts, Outsides, Insides, Lasts). This is the order we multiply in.

• First terms: `2x*x=2x^2`
• Outside terms: `2x*-5=-10x`
• Inside terms: `1*x=x`
• Last terms: `1*-5=-5`

We get the following:

`2x^2-10x+x-5`

Which is equal to

`2x^2-9x-5`

Remember, this is what I had in blue. We still have the `3` on the outside:

`3color(blue)((2x^2-9x-5))`

Distributing the `3` gives us

`6x^2-27x-15`

Hope this helps!