How do you simplify (x+2)+(x-2)(2x+1)(x+2)+(x2)(2x+1)?

2 Answers
Sep 11, 2015

(x+2) + (x-2)(2x+1)= 2x^2 -2x(x+2)+(x2)(2x+1)=2x22x

Explanation:

To solve:
(x+2) + (x-2)(2x+1)(x+2)+(x2)(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)x2x=2x2

Multiply the outer terms:
x * 1 = color(blue)(x)x1=x

Multiply the inner terms:
-2 * 2x = color(blue)(-4x)22x=4x

Multiply the last terms:
-2 * 1 = color(blue)(-2)21=2

Then add them:
2x^2 + x - 4x -22x2+x4x2
=2x^2 -3x -2=2x23x2

This means that
(x-2)(2x+1) = 2x^2 -3x -2(x2)(2x+1)=2x23x2

Now we can use this to simplify the original problem:

(x+2) + (x-2)(2x+1)(x+2)+(x2)(2x+1)
= x+2 +2x^2 -3x -2=x+2+2x23x2
color(blue)(= 2x^2 -2x)=2x22x

Sep 11, 2015

2x^2-2x2x22x
color(white)("XX")XXor
2x(x-1)2x(x1)

Explanation:

color(red)((x-2)(2x+1))(x2)(2x+1)
color(white)("XXX")=color(red)(x(2x+1) - 2(2x+1))XXX=x(2x+1)2(2x+1)
color(white)("XXX")=color(red)(2x^2+x - 4x -2)XXX=2x2+x4x2
color(white)("XXX")=color(red)(2x^2 -3x -2)XXX=2x23x2

So
color(blue)((x+2))+color(red)((x-2)(2x+1))(x+2)+(x2)(2x+1)
color(white)("XXX")=color(blue)(x+2) + color(red)(2x^2-3x-2)XXX=x+2+2x23x2
color(white)("XXX")=2x^2-2xXXX=2x22x