Question

Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) - (2m³ + 5m² + 4m) + (m² - m)

Accepted Answer

First, rewrite the expression clearly by removing the parentheses, remembering to distribute the minus sign across the second group:  $$(6m^{4}$$ - $$3m^{2} + m$$) - $$(2m^{3}$$ + $$5m^{2} + 4m$$) + $$(m^{2} - m$$)$$ becomes 6m$$^{4}$$ - 3m$$^{2}$$ + m - 2m$$^{3}$$ - 5m$$^{2}$$ - 4m + m$$^{2}$$ - m. $$Next, group like terms together. Like terms are terms that have the same variable raised to the same power. Grouping gives: $$6m^{4}$$ + $$(-2m^{3}$$) + $$(-3m^{2}$$ - $$5m^{2}$$ + $$m^{2}) + (m - 4m - m$$)$$. Now, combine the coefficients of each group of like terms by adding or subtracting them: For m$$^{4}$$ terms: 6m$$^{4}$$; for m$$^{3}$$ terms: -2m$$^{3}$$; for m$$^{2}$$ terms: -3 - 5 + 1$; for m$ terms: 1 - 4 - 1$. Simplify each group by performing the arithmetic on the coefficients: Calculate the sum for m$$^{2}$$ terms and for m$ terms separately. Finally, write the simplified expression by combining all the simplified terms back together, maintaining the order from highest to lowest power.

Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) - (2m³ + 5m² + 4m) + (m² - m)

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Key Concepts

Polynomial Addition and Subtraction

Like Terms

Distributive Property