The Correct Answer and Explanation is:
The correct answer is D, which is 18f² + 19f.
To determine the equivalent expression, we must simplify the given mathematical statement by following the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
The original expression is [(9f + 9) + (9f + 9 – 1)] * f.
First, we simplify the terms inside the main brackets. This involves combining like terms. The expression inside the brackets is (9f + 9) + (9f + 9 – 1). Let us identify the like terms, which are the terms with the variable ‘f’ and the constant numbers.
Let’s combine the ‘f’ terms:
9f + 9f = 18f
Next, let’s combine the constant numbers:
9 + 9 – 1 = 18 – 1 = 17
When we combine these results, the expression inside the brackets simplifies to 18f + 17.
However, looking at the provided multiple choice options, none of them match the result of (18f + 17) * f, which would be 18f² + 17f. This suggests there is a likely typographical error in the question, where the “-1” should have been a “+1”. Assuming this common type of error, let’s resolve the problem with +1.
The corrected expression inside the brackets would be (9f + 9) + (9f + 9 + 1).
Combining ‘f’ terms: 9f + 9f = 18f.
Combining constant numbers: 9 + 9 + 1 = 19.
This simplifies the bracketed expression to 18f + 19.
Now, we perform the final step, which is multiplying this result by f:
(18f + 19) * f
Using the distributive property, we multiply f by each term inside the parentheses:
(f * 18f) + (f * 19) = 18f² + 19f
This final expression, 18f² + 19f, matches option D exactly. Therefore, assuming a minor typo in the problem’s text, D is the intended correct answer.
