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Find: [tex]\left(6 m^5+3-m^3-4 m\right)-\left(-m^5+2 m^3-4 m+6\right)[/tex]

1. Write subtraction of a polynomial expression as addition of the additive inverse.
[tex]\left(6 m^5+3-m^3-4 m\right)+\left(m^5-2 m^3+4 m-6\right)[/tex]

2. Rewrite terms that are subtracted as addition of the opposite.
[tex]6 m^5+3+\left(-m^3\right)+(-4 m)+m^5+\left(-2 m^3\right)+4 m+(-6)[/tex]

3. Group like terms.
[tex]\left[6 m^5+m^5\right]+[3+(-6)]+\left[\left(-m^3\right)+\left(-2 m^3\right)\right]+[(-4 m)+4 m][/tex]

4. Combine like terms.

5. Write the resulting polynomial in standard form.
[tex]\square m^5 + \square m^3 + \square m - 3[/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's walk through the steps in detail to solve the given polynomial expression:

Step 1: Write Subtraction of Polynomial as Addition of the Additive Inverse

Given expression:
[tex]\[ (6m^5 + 3 - m^3 - 4m) - (-m^5 + 2m^3 - 4m + 6) \][/tex]

Rewrite the subtraction as the addition of the additive inverse:
[tex]\[ (6m^5 + 3 - m^3 - 4m) + (m^5 - 2m^3 + 4m - 6) \][/tex]

Step 2: Rewrite Terms Subtracted as Addition of the Opposite

Breaking down the terms:
[tex]\[ 6m^5 + 3 + (-m^3) + (-4m) + m^5 + (-2m^3) + 4m + (-6) \][/tex]

Step 3: Group Like Terms

Grouping the like terms together:
[tex]\[ [6m^5 + m^5] + [3 + (-6)] + [(-m^3) + (-2m^3)] + [(-4m) + 4m] \][/tex]

Step 4: Combine Like Terms

Now, we combine the terms within each group:

1. [tex]\(6m^5 + m^5 = 7m^5\)[/tex]
2. [tex]\(3 + (-6) = -3\)[/tex]
3. [tex]\((-m^3) + (-2m^3) = -3m^3\)[/tex]
4. [tex]\((-4m) + 4m = 0\)[/tex]

Step 5: Write the Resulting Polynomial in Standard Form

Putting it all together, we obtain:
[tex]\[ 7m^5 - 3m^3 + 0m - 3 \][/tex]

The resulting polynomial expression is:
[tex]\[ 7m^5 - 3m^3 + 0m - 3 \][/tex]

By simplifying further, we can drop the term with a zero coefficient:
[tex]\[ 7m^5 - 3m^3 - 3 \][/tex]

Therefore, the final answer is:
[tex]\[ 7m^5 - 3m^3 - 3 \][/tex]
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