Which expression is equivalent to (13x² - 2 + 3x) + (5x - 3x²)?

Understand the Problem

The question is asking which expression is equivalent to the sum of two given polynomial expressions. This will involve combining like terms from the expressions provided.

Answer

$10x^2 + 8x - 2$

Steps to Solve

Distribute and Combine Expressions

Start with the given expressions:

$$(13x^2 - 2 + 3x) + (5x - 3x^2)$$

Distribute if necessary (in this case, there’s no need to distribute further, just combine).

Combine Like Terms

Now, identify and combine the like terms:

For $x^2$ terms: $13x^2 - 3x^2 = 10x^2$
For $x$ terms: $3x + 5x = 8x$
For constant terms: $-2$ (no other constant to combine)

Putting these together gives:

$$10x^2 + 8x - 2$$

Identify the Equivalent Expression

Now compare the combined expression $10x^2 + 8x - 2$ with the answer choices:

A: $16x^2 + 2x - 2$
B: $10x^2 + 2x - 2$
C: $10x^2 + 8x - 2$
D: $16x^2 + 8x - 2$

The expression we found matches option C.

The expression equivalent to the sum is $10x^2 + 8x - 2$.

More Information

The correct answer is obtained by properly combining like terms from the given polynomial expressions. This is a fundamental skill in algebra when dealing with polynomials.

Tips

Forgetting to combine like terms can lead to incorrect answers.
Misidentifying which terms are like terms could result in mistakes.
Neglecting to change signs correctly, especially with negative terms.

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