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Answer :
The given expression $3x25x7(x^2 + 4)$ likely contains a typo. Assuming it is $3 \times 25 \times 7(x^2 + 4)$, the simplified form is $525x^2 + 2100$. However, none of the options match this form. If the expression was meant to be a simple numerical expression that evaluates to 30, then option OD ($2+28$) would be the correct answer. Without a clear original expression, it's challenging to determine the correct answer with certainty. The most plausible answer, assuming a typo leading to a constant, is $\boxed{30}$.
### Explanation
1. Analyzing the Expression
Let's analyze the given expression: $3x25x7(x^2 + 4)$. It seems there might be a typo in the expression. Assuming the expression is meant to be $3 \times 25 \times 7(x^2 + 4)$, we can simplify it.
2. Multiplying Constants
First, let's multiply the constants: $3 \times 25 \times 7 = 525$. So, the expression becomes $525(x^2 + 4)$.
3. Distributing the Constant
Now, distribute $525$ into the parentheses: $525(x^2 + 4) = 525x^2 + 525 \times 4 = 525x^2 + 2100$.
4. Alternative Interpretation 1
Now, let's consider the possibility that the expression was meant to be $3x + 25x - 7(x^2 + 4)$. In this case, we have $3x + 25x - 7(x^2 + 4) = 28x - 7x^2 - 28 = -7x^2 + 28x - 28$.
5. Alternative Interpretation 2
Another possibility is that the expression was meant to be $(3 + 25 - 7)(x^2 + 4)$. In this case, we have $(3 + 25 - 7)(x^2 + 4) = (28 - 7)(x^2 + 4) = 21(x^2 + 4) = 21x^2 + 84$.
6. Comparing with Options
Let's analyze the options provided:
OA. $-4x^2 + 5x - 28$
OB. $-4x^2 + 5x4$ (This seems to have a typo, let's assume it is $-4x^2 + 5x - 4$)
OC. $x^2 + 4$
OD. $2 + 28 = 30$
None of our simplified expressions exactly match the options. However, if the original expression was simply $(3+25-7)(x^2+4) = 21(x^2+4) = 21x^2 + 84$, none of the options match. If the original expression was a typo and meant to be a simple numerical expression, then option OD is a possibility.
7. Final Answer and Conclusion
Given the options, it's most likely that there's a typo in the original question or in the options. However, if we consider option OD, $2+28 = 30$, this is a constant. If the original expression was meant to simplify to a constant, then this might be the correct answer. However, without a clear original expression, it's hard to determine the correct answer with certainty. Assuming the original expression was a typo and meant to be a simple numerical expression that evaluates to 30, then the answer would be D.
### Examples
In simplifying algebraic expressions, we often encounter scenarios where we need to combine like terms or distribute constants. This skill is crucial in various fields, such as physics, where we might need to simplify equations describing motion or forces. For instance, if we have an equation representing the total energy of a system, simplifying it allows us to easily identify the different components and their contributions. Similarly, in economics, simplifying cost or revenue functions helps in making informed business decisions.
### Explanation
1. Analyzing the Expression
Let's analyze the given expression: $3x25x7(x^2 + 4)$. It seems there might be a typo in the expression. Assuming the expression is meant to be $3 \times 25 \times 7(x^2 + 4)$, we can simplify it.
2. Multiplying Constants
First, let's multiply the constants: $3 \times 25 \times 7 = 525$. So, the expression becomes $525(x^2 + 4)$.
3. Distributing the Constant
Now, distribute $525$ into the parentheses: $525(x^2 + 4) = 525x^2 + 525 \times 4 = 525x^2 + 2100$.
4. Alternative Interpretation 1
Now, let's consider the possibility that the expression was meant to be $3x + 25x - 7(x^2 + 4)$. In this case, we have $3x + 25x - 7(x^2 + 4) = 28x - 7x^2 - 28 = -7x^2 + 28x - 28$.
5. Alternative Interpretation 2
Another possibility is that the expression was meant to be $(3 + 25 - 7)(x^2 + 4)$. In this case, we have $(3 + 25 - 7)(x^2 + 4) = (28 - 7)(x^2 + 4) = 21(x^2 + 4) = 21x^2 + 84$.
6. Comparing with Options
Let's analyze the options provided:
OA. $-4x^2 + 5x - 28$
OB. $-4x^2 + 5x4$ (This seems to have a typo, let's assume it is $-4x^2 + 5x - 4$)
OC. $x^2 + 4$
OD. $2 + 28 = 30$
None of our simplified expressions exactly match the options. However, if the original expression was simply $(3+25-7)(x^2+4) = 21(x^2+4) = 21x^2 + 84$, none of the options match. If the original expression was a typo and meant to be a simple numerical expression, then option OD is a possibility.
7. Final Answer and Conclusion
Given the options, it's most likely that there's a typo in the original question or in the options. However, if we consider option OD, $2+28 = 30$, this is a constant. If the original expression was meant to simplify to a constant, then this might be the correct answer. However, without a clear original expression, it's hard to determine the correct answer with certainty. Assuming the original expression was a typo and meant to be a simple numerical expression that evaluates to 30, then the answer would be D.
### Examples
In simplifying algebraic expressions, we often encounter scenarios where we need to combine like terms or distribute constants. This skill is crucial in various fields, such as physics, where we might need to simplify equations describing motion or forces. For instance, if we have an equation representing the total energy of a system, simplifying it allows us to easily identify the different components and their contributions. Similarly, in economics, simplifying cost or revenue functions helps in making informed business decisions.
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