Question
Subtract polynomials: $ \, \color{blue}{ 6x^2+2x^3 } \, $ , $ \, \color{orangered}{ -x^2-6x^3-3x }$.
Answer
$$ \left( \color{blue}{6x^2+2x^3} \right) - \left( \color{orangered}{-x^2-6x^3-3x} \right) = 8x^3+7x^2+3x $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 2x^3+6x^2 \\ Q(x) &= -6x^3-x^2-3x \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 2x^3 & 6x^2 & \\ \color{red}{ - } & -6x^3 & -x^2 & -3x \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & 2x^3 & 6x^2 & \\ \color{red}{ - } & 6x^3 & x^2 & 3x \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 2x^3 & 6x^2 & \\ \color{red}{ - } & 6x^3 & x^2 & 3x \\ \hline & -4x^3 & 5x^2 & -3x \end{array} $$This page was created using
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