Simplify the following expression: ![Screenshot 2025-05-06 202502.png](https://res.cloudinary.com/aptidude/image/upload/v1746543310/aptidude_questions/v0ctrfjf7zapxa84xj6b.png)

Question

Accepted Answer

Let's simplify the expression step by step:

Given:
$$(\frac{3}{a} + 3a)\left(\frac{9}{a^2} - 9 + 9a^2\right)$$

Step 1: Substitute a = 1 into the expression.

First term: $\frac{3}{a} + 3a = \frac{3}{1} + 3 \times 1 = 3 + 3 = 6$

Second term: $\frac{9}{a^2} - 9 + 9a^2 = \frac{9}{1^2} - 9 + 9 \times 1^2 = 9 - 9 + 9 = 9$

Step 2: Multiply the two results:
$$6 \times 9 = 54$$

Step 3: The answer is 54.

However, the options are all decimals (1.27, 2.63, 3.81, 4.54), which suggests a possible misinterpretation. Let's double-check the calculation.

Let's check if the original expression is written correctly or if there is a decimal point missing in the coefficients. If the question is as given, the answer is 54, which does not match any options.

But since the correct answer is marked as 4.54, perhaps the expression is:
$$(\frac{3}{a} + 3a)\left(\frac{9}{a^2} - 9 + 9a^2\right)$$ with a = 1

Let's try evaluating with decimal values:

First term: $\frac{3}{1} + 3 \times 1 = 3 + 3 = 6$
Second term: $\frac{9}{1^2} - 9 + 9 \times 1^2 = 9 - 9 + 9 = 9$

So, $6 \times 9 = 54$

But the answer is 4.54, which suggests the decimal point is misplaced in the options. The correct calculation is 54.

Therefore, the correct answer is 54, but as per the options, 4.54 is marked as correct. This may be a typographical error in the options. The step-by-step calculation confirms the answer is 54.

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