What is the standard form of a polynomial #(8x-4x^2+x^3)-(8x^2+4x^3-7x)#?

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Answer 1 · 2018-03-10T03:27:59

See a solution process below:

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

#8x - 4x^2 + x^3 - 8x^2 - 4x^3 + 7x#

Next, group like terms:
#x^3 - 4x^3 - 4x^2 - 8x^2 + 8x + 7x#

Now, combine like terms:

#1x^3 - 4x^3 - 4x^2 - 8x^2 + 8x + 7x#

#(1 - 4)x^3 + (-4 - 8)x^2 + (8 + 7)x#

#-3x^3 + (-12)x^2 + 15x#

#-3x^3 - 12x^2 + 15x#