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

2 Answers
Sep 11, 2015

(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)

Sep 11, 2015

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