Subtract polynomials: $ \, \color{blue}{ 6x+8x-5x-3 } \, $ , $ \, \color{orangered}{ -3x+10x-4 }$.

$$ \left( \color{blue}{6x+8x-5x-3} \right) - \left( \color{orangered}{-3x+10x-4} \right) = 2x+1 $$

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

$$ \begin{aligned} P(x) &= 9x-3 \\ Q(x) &= 7x-4 \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & 9x & -3 \\ \color{red}{ - } & 7x & -4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 9x & -3 \\ \color{red}{ - } & -7x & 4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 9x & -3 \\ \color{red}{ - } & -7x & 4 \\ \hline & 16x & -7 \end{array} $$

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