# Subtract the polynomials using the horizontal format. 2x^3+x^2-7x-2 from 5x^3+2x^2+6x-13

Subtract the polynomials using the horizontal format. $$\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}$$ from $$\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}$$

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The given two polynomials are, $$\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}$$ and $$\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}$$
We need to subtract $$\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}$$ from $$\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}$$
On combining the like terms, we simplify the given expression.
On simplifying the given expression, we get
$$\displaystyle{\left({5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}\right)}-{\left({2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}\right)}={5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}-{2}{x}^{{3}}-{x}^{{2}}+{7}{x}+{2}$$
$$\displaystyle-{\left({5}-{2}\right)}{x}^{{3}}+{\left({2}-{1}\right)}{x}^{{2}}+{\left(-{13}+{2}\right)}$$
$$\displaystyle={3}{x}^{{3}}+{x}^{{2}}-{11}$$
Therefore, the resultant expression is $$\displaystyle{3}{x}^{{3}}+{x}^{{2}}-{11}$$