Consider the given expression,
[tex](-4x^3-4x^2-3x+2)(x+6)[/tex]
In order to simplify the expression, the first factor is multiplied by 'x' and then '6'. Finally, all the terms will be added,
[tex]=x(-4x^3-4x^2-3x+2)+6(-4x^3-4x^2-3x+2)[/tex]
The given table gives each of the above products. So we can substitute the values from there,
[tex]=-4x^4-4x^3-3x^2+2x-24x^3-24x^2-18x+12[/tex]
Adding the like terms,
[tex]\begin{gathered} =-4x^4+(-4-24)x^3+(-3-24)x^2+(2-18)x+12 \\ =-4x^4-28x^3-27x^2-16x+12 \end{gathered}[/tex]
Thus, the simplified form of the given expression is,
[tex]-4x^4-28x^3-27x^2-16x+12[/tex]
