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Simplify x2 + x + 3 – 4x – 4x2 – 10 by combining like terms.

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2 Answers

x2 + x + 3 - 4x -4x2 - 10
 
"Like terms" are terms that contain the same variables raised to the same power, such as x2.  Only the numerical coefficients are different (3x2, -5x2, etc.).  The first step is to group the like terms.  I've added parentheses to make it clear, but the parentheses are not required:
 
(x2 - 4x2) + (x - 4x) + (3 -10)
 
Here x2 and -4x2 are like terms, x and -4x are like terms, and 3 and -10 are like terms.  Next simplify by adding or subtracting the like terms:
 
x2 - 4x2 = -3x2
x - 4x = -3x
3 - 10 = -7
 
x2 + x + 3 - 4x -4x2 - 10 =  (x2 - 4x2) + (x - 4x) + (3 -10) = -3x2 - 3x - 7
x2 + x + 3 – 4x – 4x2 – 10 
 
Re-writing the expression so that like terms are grouped, yields
 
(x2 - 4x2) + (x-4x) +(3-10)
 
Simplifying the like terms , the final expression is
 
-3x2 -3x -7