Subtract polynomials: $ \, \color{blue}{ -10x^3+5x^3+6 } \, $ , $ \, \color{orangered}{ 4x^3+2x }$.

$$ \left( \color{blue}{-10x^3+5x^3+6} \right) - \left( \color{orangered}{4x^3+2x} \right) = -9x^3-2x+6 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -5x^3+6 \\ Q(x) &= 4x^3+2x \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrr} & -5x^3 & & 6 \\ \color{red}{ - } & 4x^3 & 2x & \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrrr} & -5x^3 & & 6 \\ \color{red}{ - } & -4x^3 & -2x & \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrrr} & -5x^3 & & 6 \\ \color{red}{ - } & -4x^3 & -2x & \\ \hline & -x^3 & 2x & 6 \end{array} $$

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