How do you simplify #(x^2 -6x + 5) - (x^2 + x - 2)#?

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Answer 1 · 2016-09-04T17:48:39

#-7x+7#

#(x^2 -6x + 5) - (x^2 + x - 2)#

"Subtracting is the same as adding on the inverse"
"The minus sign outside the bracket will change the signs inside"

These both tell us that when the second bracket is removed, the signs of the terms inside will change.

#(x^2 -6x + 5) - (x^2 + x - 2)#

= # color(red)(x^2) color(blue)(-6x) color(lime)(+ 5) color(red)(- x^2) color(blue)(- x) color(lime)(+ 2) " "larr # collect like terms.

=#color(red)(x^2)color(red)(- x^2)color(blue)(-6x)color(blue)(- x)color(lime)(+ 5) color(lime)(+ 2) #

=#-7x+7#