Subtract polynomials: $ \, \color{blue}{ 4x^3+5 } \, $ , $ \, \color{orangered}{ 7-2x^3 }$.

$$ \left( \color{blue}{4x^3+5} \right) - \left( \color{orangered}{7-2x^3} \right) = 6x^3-2 $$

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

$$ \begin{aligned} P(x) &= 4x^3+5 \\ Q(x) &= -2x^3+7 \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & 4x^3 & 5 \\ \color{red}{ - } & -2x^3 & 7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 4x^3 & 5 \\ \color{red}{ - } & 2x^3 & -7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 4x^3 & 5 \\ \color{red}{ - } & 2x^3 & -7 \\ \hline & 2x^3 & 12 \end{array} $$

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