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Simplify [tex]\left(-6x^4 - 5x^3 + x^2\right) + \left(4x^2 + 6x^4 - 4x^5\right)[/tex].

A. [tex]-9x^3 + 5x^2[/tex]
B. [tex]12x^4 - 9x^3 + 5x^2[/tex]
C. [tex]-x^3 + 5x^2[/tex]
D. [tex]-9x^3 - 5x^2[/tex]

Answer :

To simplify the given expression, [tex]\((-6x^4 - 5x^3 + x^2) + (4x^2 + 6x^4 - 4x^5)\)[/tex], we'll combine the like terms. Let's break down the expression step by step:

1. Write down the entire expression:

[tex]\((-6x^4 - 5x^3 + x^2) + (4x^2 + 6x^4 - 4x^5)\)[/tex]

2. Rearrange and group the like terms:

[tex]\[
(-6x^4 + 6x^4) - 5x^3 + (x^2 + 4x^2) - 4x^5
\][/tex]

3. Combine the like terms:

- The [tex]\(x^4\)[/tex] terms: [tex]\(-6x^4 + 6x^4 = 0\)[/tex]
- The [tex]\(x^3\)[/tex] term remains: [tex]\(-5x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(x^2 + 4x^2 = 5x^2\)[/tex]
- The [tex]\(x^5\)[/tex] term remains: [tex]\(-4x^5\)[/tex]

4. Write the expression with the combined terms:

[tex]\[-4x^5 - 5x^3 + 5x^2\][/tex]

The simplified expression is:

[tex]\[
-4x^5 - 5x^3 + 5x^2
\][/tex]

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