College

Add the following expressions:

1) [tex]\left(6x^5 - 3x^4 - 3x\right) + \left(5x^5 + 8x^4 + 8x\right)[/tex]

Choose the correct answer:

A) [tex]11x^5 + 5x^4 + 5x[/tex]
B) [tex]2x^5 + 14x^4 + 5x[/tex]
C) [tex]21x^{10}[/tex]
D) [tex]11x + 5x^5 + 5x^4[/tex]

Answer :

We need to simplify the expression
[tex]$$
\left(6 x^5-3 x^4-3 x\right)+\left(5 x^5+8 x^4+8 x\right).
$$[/tex]

### Step 1. Group Like Terms

Group the terms with the same power of [tex]$x$[/tex]:

- For [tex]$x^5$[/tex]: [tex]$$6x^5 + 5x^5$$[/tex]
- For [tex]$x^4$[/tex]: [tex]$$-3x^4 + 8x^4$$[/tex]
- For [tex]$x$[/tex]: [tex]$$-3x + 8x$$[/tex]

### Step 2. Combine the Terms

Now, add the coefficients for each group:

- [tex]$x^5$[/tex] terms:
[tex]$$
6x^5 + 5x^5 = 11x^5
$$[/tex]

- [tex]$x^4$[/tex] terms:
[tex]$$
-3x^4 + 8x^4 = 5x^4
$$[/tex]

- [tex]$x$[/tex] terms:
[tex]$$
-3x + 8x = 5x
$$[/tex]

### Step 3. Write the Final Answer

After combining all like terms, the simplified expression is:
[tex]$$
11x^5 + 5x^4 + 5x.
$$[/tex]

Thus, the correct answer is:

[tex]$$
11 x^5+5 x^4+5 x.
$$[/tex]

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