Question

How do you simplify `(x+2)+(x-2)(2x+1)`?

Answer 1

`(x+2) + (x-2)(2x+1)= 2x^2 -2x`

Explanation:

To solve:
`(x+2) + (x-2)(2x+1)`,
first multiply the two binomials on the right.

We can use the FOIL method here:

Mulitply the first terms:
`x* 2x = color(blue)(2x^2)`

Multiply the outer terms:
`x * 1 = color(blue)(x)`

Multiply the inner terms:
`-2 * 2x = color(blue)(-4x)`

Multiply the last terms:
`-2 * 1 = color(blue)(-2)`

Then add them:
`2x^2 + x - 4x -2`
`=2x^2 -3x -2`

This means that
`(x-2)(2x+1) = 2x^2 -3x -2`

Now we can use this to simplify the original problem:

`(x+2) + (x-2)(2x+1)`
`= x+2 +2x^2 -3x -2`
`color(blue)(= 2x^2 -2x)`

Answer 2

`2x^2-2x`
`color(white)("XX")`or
`2x(x-1)`

Explanation:

`color(red)((x-2)(2x+1))`
`color(white)("XXX")=color(red)(x(2x+1) - 2(2x+1))`
`color(white)("XXX")=color(red)(2x^2+x - 4x -2)`
`color(white)("XXX")=color(red)(2x^2 -3x -2)`

So
`color(blue)((x+2))+color(red)((x-2)(2x+1))`
`color(white)("XXX")=color(blue)(x+2) + color(red)(2x^2-3x-2)`
`color(white)("XXX")=2x^2-2x`