Question 73971: Simplify: (3x^2 + 6x - 8) + (-5x^2 - 8x + 4)
A) -2x^2 - 14x -12
B) -2x^2 - 2x - 4
C) 3x^2 + 2x + 12
D) 8x^2 + 14x + 12
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! (3x^2 + 6x - 8) + (-5x^2 - 8x + 4)
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If the parentheses that group the terms are preceded by a + sign or no sign which is to be taken
as a + sign, you can just remove the parentheses without changing the signs of the terms that
are inside them.
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Since the two sets of parentheses above are preceded by + or no sign, you can just remove them
to get:
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3x^2 + 6x - 8 -5x^2 - 8x + 4
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You can only combine terms that contain the same x's. So you can combine 3x^2 and - 5x^2 because
they both contain x^2. The +3 and the -5 combine to give you -2 and you multiply that
by the x^2 to get -2x^2. This is one of the terms in the answer.
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Next combine the two terms that just contain x. These terms are +6x and -8x. The +6 and -8
add to give you -2 and this multiplies x. So the answer is -2x. You now have two terms of
the answer ... -2x^2 - 2x.
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Finally, combine the two terms that contain no x's ... -8 and +4. They add to -4, and that
is the third term of the answer. The whole answer, therefore, is -2x^2 - 2x - 4.
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Answer B is the correct answer.
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All this problem involved was watching for like terms involving x and combining them by the
rules of algebraic addition of numbers. Hope you're gaining some insight into how the process
works.
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