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

2 Answers
Sep 11, 2015

Answer:

#(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

Answer:

#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#