How do you simplify #\frac { 2} { 3} ( x - x ^ { 2} ) + ( x + 1) ( x + 2)#?

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Answer 1 · 2017-11-13T06:51:12

#1/3x +11/3x+2#

#2/3(x-x^2)+(x+1)(x+2)#

Remove the brackets by multiplying.

#= 2/3x-2/3x^2 + x^2 +2x+x+2#

Collect the like terms.

#=color(blue)(-2/3x^2 +x^2) +color(red)(2/3x+2x+x) +color(green)(2)#

#= color(blue)(1/3x^2) +color(red)(11/3x)+color(green)(2)#

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For clarity: #color(blue)(-2/3x^2 +x^2)#

#color(blue)(-2/3 + 1 = -1 2/3 = 1/3)#

and

#color(red)(2/3x+2x+x = (3 2/3)x)#

However we do not usually use mixed numbers in algebra, so change to an improper fraction.

#3 2/3 = 11/3#