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(3x^4 - 2x^3 + 4x - 2) + (3x^3 - 2x^2- x + 4)

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1 Answer

1) Open up parentheses. If there is '+' sign in front, just drop parentheses and keep signs of all terms inside unchanged. Otherwise, if there is '-' sign in front, drop parentheses and that '-' sign and change sign of every term inside parentheses.
 
In your case,
(3x4-2x3+4x-2)+(3x3-2x2-x+4)=3x4-2x3+4x-2+3x3-2x2-x+4;
 
2) Now collect like terms, that is terms with the same powers of x. In your case those are:
 
-2x3 and 3x3; 4x and -x; -2 and 4.
 
3x4-2x3+4x-2+3x3-2x2-x+4
 
Here I underlined like terms and marked them with different colors.
 
Combining like terms is done like this:
-2x3+3x3=(-2+3)*x3=1*x3=x3.
 
I took common factor (x3 in this case) out using distributive property of multiplication.
 
Similarly, 4x-x=3x and -2+4=2.
 
So, the final result is:
3x4+x3-2x2+3x+2