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Frank thinks that 2x + 3x² is the same as 5x³. Which statement shows that it is not the same? In Imagin Math.

a) 2 + 3x = 5x
b) 2x + 3x² ≠ 5x³
c) 2x + 3x = 5
d) (2x)² + 3 = 5x³

1 Answer

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Final answer:

The correct statement showing that 2x + 3x² is not the same as 5x³ is b) 2x + 3x² ≠ 5x³. These terms, with different exponents, cannot simply be added together to form a new term with a summed exponent.

Step-by-step explanation:

Frank thinks that 2x + 3x² is the same as 5x³. The statement that shows these expressions are not the same is b) 2x + 3x² ≠ 5x³. Algebraic expressions must follow the law of exponents and cannot be combined unless they have the same bases and exponents. The terms 2x and 3x² cannot be combined to make 5x³ because they don't have the same exponent. For instance, when multiplying numbers with the same base, we add their exponents; for example, 5± × 5± becomes , which is 25, not 5. When facing different powers of the same variable, such as in 2x and 3x², they remain separate terms as the exponents differ.

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