Question

How do you write in standard form `y = 4(x + 5) - 2(x + 1)(x + 1)`?

Answer 1

`-2x^2+18`

Explanation:

Since this expression has many parts, I will color-code it and tackle it one by one.

`color(purple)(4(x+5))-2color(steelblue)((x+1)(x+1)`

For the expression in purple, all we need to do is distribute the `4` to both terms in the parenthesis. Doing this, we now have

`color(purple)(4x+20)-2color(steelblue)((x+1)(x+1))`

What I have in blue, we can multiply with the mnemonic FOIL, which stands for Firsts, Outsides, Insides, Lasts. This is the order we multiply the terms in.

Foiling `(x+1)(x+1)`:

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

This simplifies to `color(steelblue)(x^2+2x+1)`. We now have

`color(purple)(4x+20)-2(color(steelblue)(x^2+2x+1))`

Distributing the `-2` to the blue terms gives us

`color(purple)(4x+20)-color(steelblue)(2x^2-4x-2)`

Combining like terms gives us

`-2x^2+18`

We see that our polynomial is in standard form, `ax^2+bx+c`. Notice that the `x` terms cancel out, so we don't have a `bx` term.

Hope this helps!