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

Question

Nathan Axel · Accepted Answer

#-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#

Hazel Anglin · Answer

undefined To simplify the expression $ (x^2 - 6x + 5) - (x^2 + x - 2) $, you distribute the negative sign inside the second parenthesis and then combine like terms:

$ (x^2 - 6x + 5) - (x^2 + x - 2) $
$ = x^2 - 6x + 5 - x^2 - x + 2 $

Now, combine like terms:

$ = (x^2 - x^2) + (-6x - x) + (5 + 2) $
$ = 0x^2 - 7x + 7 $
$ = -7x + 7 $

So, the simplified expression is $ -7x + 7 $.

Jace Anderson · Answer

undefined To simplify $(x^2 - 6x + 5) - (x^2 + x - 2)$, you first distribute the negative sign inside the parentheses of the second expression. Then, combine like terms. This yields $(x^2 - 6x + 5) - x^2 - x + 2$. Next, combine like terms by grouping the terms with the same variables. This results in $x^2 - x^2 - 6x - x + 5 + 2$. Finally, simplify the expression further by performing arithmetic operations. Thus, $x^2 - x^2$ cancels out, leaving $-6x - x$, which simplifies to $-7x$. Adding the constants gives $5 + 2 = 7$. Hence, the simplified expression is $-7x + 7$.