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What is the simplified form of the expression [tex](8x^2 - 3x + 1) + (2x^3 - 2x^2 - 5x - 8)[/tex]?

A) [tex]2x^3 - 2x - 7[/tex]
B) [tex]2x^3 + 5x - 7[/tex]
C) [tex]10x^3 - 2x^2 - 8x - 7[/tex]
D) [tex]10x^3 - 5x^2 - 8x - 7[/tex]

Answer :

Final answer:

The simplified form of the expressions (8x² - 3x + 1) and (2x³ - 2x² - 5x - 8) is 2x³ + 6x² - 8x - 7. But this answer doesn't match any of the choices provided in the question. The question or the answer choices could have a mistake.

Explanation:

The simplified form of the expression (8x² - 3x + 1) + (2x³ - 2x² - 5x - 8) is attained by combining like terms from both expressions. In mathematics, combining like terms is a technique used to simplify expressions or equations. The like terms in the given expressions are x³, x², x, and the constants (numbers on their own). Always ensure to keep track of the sign before each term while combining.

For this specific problem, there's only one cubed term, 2x³. Then, for the squared terms, combine 8x² and -2x² to get 6x². Next, combine -3x (from the first expression) and -5x(from the second expression) to get -8x. Lastly, combine 1 (from the first expression) and -8 (from the second) to get -7.

So, the simplified form of the given expressions will be: 2x³ + 6x² - 8x - 7. However, this does not match any of the answer choices you’ve listed in your question. Please confirm if there's an error in the question or the answer choices.

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