How do you simplify #(3x ^ { 2} + 8x - 7) - ( 5x ^ { 2} - 2- 11)#?

2 Answers
smendyka
Oct 31, 2017

See a solution process below:

Explanation:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

#3x^2 + 8x - 7 - 5x^2 + 2 + 11#

Next, group like terms:

#3x^2 - 5x^2 + 8x - 7 + 2 + 11#

Now, combine like terms:

#(3 - 5)x^2 + 8x + (-7 + 2 + 11)#

#-2x^2 + 8x + 6#

If this is supposed to be:

#(3x^2 + 8x - 7) - (5x^2 - 2color(red)(x) - 11)#

We can use the same process:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

#3x^2 + 8x - 7 - 5x^2 + 2x + 11#

Next, group like terms:

#3x^2 - 5x^2 + 8x + 2x - 7 + 11#

Now, combine like terms:

#(3 - 5)x^2 + (8 + 2)x + (-7 + 11)#

#-2x^2 + 10x + 4#

Shantelle
Oct 31, 2017

#-2x^2 + 8x + 6#

Explanation:

The original equation is #(3x^2 + 8x - 7) - (5x^2 - 2 - 11)#.

The first thing we do is simplify the #-2# and #-11#.
#3x^2 + 8x - 7 - (5x^2 - 13)#
Notice that the negative applies to everything inside that parenthesis.
#3x^2 + 8x - 7 - 5x^2 + 13#

Now we need to "combine like terms."

#3x^2# is a "friend" of #-5x^2#, so we add them up.

#8x# doesn't have "friends" so we leave him alone.

#-7# is "friends" with #13# so we add them up.

Finally, this is our solution:
#-2x^2 + 8x + 6#

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