How can 5(3 + 2) be expressed using the distributive
property?
A 5(3) x 5(2)
B (5 x 3) x (5 x 2)
C 5(3) + 5(2)
D (5+3)x (5+2)
The Correct Answer and Explanation is:
The correct answer is C: 5(3) + 5(2).
Explanation:
The distributive property is a fundamental concept in algebra that involves distributing a number across an addition or subtraction within parentheses. It is typically expressed in the form:
[
a(b + c) = a \cdot b + a \cdot c
]
In this case, the expression 5(3 + 2) involves multiplying 5 by the sum of 3 and 2. According to the distributive property, instead of adding 3 and 2 first and then multiplying the result by 5, you can distribute the multiplication over the addition. This means multiplying 5 by each term inside the parentheses individually.
So, applying the distributive property to 5(3 + 2), we get:
[
5(3 + 2) = 5 \cdot 3 + 5 \cdot 2
]
This simplifies to:
[
5(3) + 5(2)
]
Thus, C: 5(3) + 5(2) is the correct answer because it represents the application of the distributive property.
Why the other answers are incorrect:
- A: 5(3) x 5(2): This suggests that the two terms inside the parentheses should be multiplied together (5(3) multiplied by 5(2)), which is not the distributive property. Instead, it suggests a multiplication of two separate terms, which does not reflect the original expression.
- B: (5 x 3) x (5 x 2): This is incorrect because it also changes the structure of the original expression. The distributive property only involves distributing the multiplication over the sum, not multiplying the results of the individual terms inside parentheses first and then multiplying them together.
- D: (5 + 3) x (5 + 2): This is not correct because it misrepresents the original expression. Instead of distributing the multiplication over the addition, it incorrectly changes the addition to occur inside separate parentheses, leading to an entirely different operation.
Thus, C: 5(3) + 5(2) correctly expresses the distributive property applied to 5(3 + 2).