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To calculate the product of the given trinomials, we will use the Distributive Property.
The next 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.
$4x_{6}+12x_{4}+16x_{3}−8x_{5}−24x_{3}−32x_{2}−2x_{4}−6x_{2}−8x $
In this case, we have one $x_{6}-term,$ one $x_{5}-terms,$ two $x_{4}-terms,$ two $x_{3}-terms,$ two $x_{2}-terms,$ and one $x-term.$ To simplify the expression we will rearrange the terms and then evaluate the sum or difference of the like terms.

$(4x_{2}−8x−2)(x_{4}+3x_{2}+4x)$

MultParMultiply parentheses

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

DistrDistribute $4x_{2}$

$4x_{6}+12x_{4}+16x_{3}−8x(x_{4}+3x_{2}+4x)−2(x_{4}+3x_{2}+4x)$

DistrDistribute $-8x$

$4x_{6}+12x_{4}+16x_{3}−8x_{5}−24x_{3}−32x_{2}−2(x_{4}+3x_{2}+4x)$

DistrDistribute $-2$

$4x_{6}+12x_{4}+16x_{3}−8x_{5}−24x_{3}−32x_{2}−2x_{4}−6x_{2}−8x$

$4x_{6}+12x_{4}+16x_{3}−8x_{5}−24x_{3}−32x_{2}−2x_{4}−6x_{2}−8x$

CommutativePropAddCommutative Property of Addition

$4x_{6}−8x_{5}+12x_{4}−2x_{4}+16x_{3}−24x_{3}−32x_{2}−6x_{2}−8x$

AddSubTermsAdd and subtract terms

$4x_{6}−8x_{5}+10x_{4}−8x_{3}−38x_{2}−8x$