How do you simplify #(6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)#?

1 Answer
Tony B
Dec 16, 2016

#x^3+6x^2+2x+13#

Explanation:

Write as:#" "+1(6x^2-3+5x^3) -1(4x^3-2x-16)#

The 1's in front of the brackets are not normally written.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Multiply everything inside the left brackets by +1")#

#6x^2-3+5x^3#

Ordering these gives

#color(blue)(5x^3+6x^2-3)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Multiply everything inside the right brackets by -1")#

#color(blue)(-4x^3+2x+16)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting everything together")#

#5x^3+6x^2-3" "-4x^3+2x+16#

Collecting like terms:

#(5x^3-4x^3)+6x^2+2x+(16-3)#

#color(blue)(x^3+6x^2+2x+13)#

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