How do you combine #(2x - 4- 2x ^ { 4} ) - ( 5+ 4x ^ { 4} - 7x ) - ( 7+ 7x ^ { 4} )#?

1 Answer
Feb 12, 2018

The answer is #-13x^4+9x-16#.

Explanation:

You can think of the minus sign in front of those parentheses as a #-1# because that would keep everything the same. Then, apply the distributive property.

#(2x-4-2x^4)-(5+4x^4-7x)-(7+7x^4)#

#(2x-4-2x^4)-1(5+4x^4-7x)-1(7+7x^4)#

#(2x-4-2x^4)-1(5+4x^4-7x)-7-7x^4#

#(2x-4-2x^4)-5-4x^4+7x-7-7x^4#

You can remove these parentheses because there is nothing that they need to be affected by.

#2x-4-2x^4-5-4x^4+7x-7-7x^4#

Now, combine the like terms.

#color(red)(2x)color(blue)(-4)color(green)(-2x^4)color(blue)(-5)color(green)(-4x^4)+color(red)(7x)color(blue)(-7)color(green)(-7x^4)#

#color(green)(-2x^4-4x^4-7x^4)+color(red)(2x+7x)color(blue)(-4-5-7)#

#color(green)(-13x^4)+color(red)(9x)color(blue)(-16)#

That is your final answer.