College

Which expression is the simplest form of [tex]3x^3 + x^2 + 2(x^3 − 4x^2)[/tex]?

A. [tex]5x^3 - 7x^2[/tex]
B. [tex]5x^3 - 7x^2[/tex]
C. [tex]5x^3 - 7x^2[/tex]
D. [tex]5x^3 - 7x^2[/tex]

Answer :

Final answer:

The simplest form of the expression 3x³ + x² + 2 (x³ − 4x²) is 5x³ - 7x².


Explanation:

To simplify the expression 3x³ + x² + 2 (x³ − 4x²), we first distribute the 2 to the terms inside the parentheses. This gives us: 3x³ + x² + 2x³ − 8x². We can then combine like terms by adding the coefficients of x³ and x² separately: 3x³ + 2x³ + x² − 8x².

When we combine the like terms, we add the coefficients of x³, which gives us 5x³, and we also add the coefficients of x², which gives us -7x². Therefore, the simplest form of the given expression is 5x³ - 7x².


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