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The first step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable and the same exponent — can be combined.
$(12x_{5}−3x_{4}+2x−5)+(8x_{4}−3x_{3}+4x+1) $
In this case, we have one $x_{5}-term,$ two $x_{4}-terms,$ one $x_{3}-term,$ two $x-terms,$ and two $constants.$ To simplify the expression we will rearrange the terms and then combine like terms.

$(12x_{5}−3x_{4}+2x−5)+(8x_{4}−3x_{3}+4x+1)$

RemoveParRemove parentheses

$12x_{5}−3x_{4}+2x−5+8x_{4}−3x_{3}+4x+1$

CommutativePropAddCommutative Property of Addition

$12x_{5}−3x_{4}+8x_{4}−3x_{3}+4x+2x+1−5$

AddSubTermsAdd and subtract terms

$12x_{5}+5x_{4}−3x_{3}+6x−4$