Question

Find: (6m5 3 â€"" m3 â€"" 4m) â€"" (â€""m5 2m3 â€"" 4m 6) Write subtraction of a polynomial expression as addition of the additive inverse. (6m5 3 â€"" m3 â€"" 4m) (m5 â€"" 2m3 4m â€"" 6) Rewrite terms that are subtracted as addition of the opposite. 6m5 3 (â€""m3) (â€""4m) m5 (â€""2m3) 4m (â€""6) Group like terms. [6m5 m5] [3 (â€""6)] [(â€""m3) (â€""2m3)] [(â€""4m) 4m] Combine like terms. Write the resulting polynomial in standard form. M5 â€"" m3 m â€"" 3.

Answer 1

The subtraction in the standard form of the polynomial is $\rm 7m^5-3m^2-3$.

Given that

Expression; $\rm (6m^5 + 3 - m^3 -4m) -(-m^5 + 2m^3 - 4m + 6)$.

We have to determine

The subtraction of a polynomial.

According to the question

Expression; $\rm (6m^5 + 3 - m^3 -4m) -(-m^5 + 2m^3 - 4m + 6)$.

To find the subtraction of the polynomial follow all the steps given below.

• Step1; Write the expression as an additive inverse.

                   $\rm (6m^5 + 3 - m^3 -4m) -(-m^5 + 2m^3 - 4m + 6)\\\\\rm (6m^5 + 3 - m^3 -4m) +(m^5 -2m^3 +4m - 6)$

• Step2; Rewrite terms that are subtracted as the addition of the opposite.

        $\rm (6m^5 + 3 - m^3 -4m) +(m^5 -2m^3 +4m - 6)\\\\6m^5 + 3 + (-m^3) + (-4m) + m^5 + (2m^3) + 4m + (-6)$

• Step3; Group-like terms.

                   $\rm 6m^5 + 3 + (-m^3) + (-4m) + m^5 + (2m^3) + 4m + (-6)\\\\(6m^5 + m^5) + [3 + (-6)] + [(-m^3) + (-2m^3)] + [(-4m) + 4m]$

• Step4; the resulting polynomial in standard form is,

                    $\rm (6m^5 + m^5) + [3 + (-6)] + [(-m^3) + (-2m^3)] + [(-4m) + 4m]\\\\ 7m^5-3m^2-3$

                   

Hence, the subtraction in the standard form of the polynomial is $\rm 7m^5-3m^2-3$.

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