Question

where does the -8x go?

Answer 1

(x+1)(x-9)=x^2 -8x-9.

The -8x didn't go anywhere :)

Answer 2

It isn’t x^2 in step three it’s just (x+1)(x-9)

You can get the expression x^2 -8x -9 from (x+1)(x-9) by multiplying.

Let’s break that down into two parts.

Part A: x*(x-9)
Part B: 1(x-9)

The x and the one come from the (x+1) and they both can be multiplied by the (x-9) separately then added together.
Part A gives us x^2 -9x

Part B gives us x-9

Then you add those together

x^2 -9x +x -9

Which gives us x^2 -8x -9.

Answer 3

When you factor it, -9 + 1 = -8.

Although it should be (x+1)(x-9).

In a form like that, when you multiply it out, you get x^2 + x -9x -9. Which is x^2 -8x + 9.

When factoring, it does the opposite.

Basically think of it as (x+a)(x+b) = x^2 + (a+b)x + (a*b). In this case, 1 and -9 are a and b, which added is -8.