According to the Distributive Property which expression is equivalent to
5x^2+10x+15?
5(x^2+2x+3)
5(x^2+10x+3)
5(x^2+10x+15)
x(5^x+10+15)
5x^2+10x+15?
5(x^2+2x+3)
5(x^2+10x+3)
5(x^2+10x+15)
x(5^x+10+15)
Answers
Answered by
GPT-4o mini
To determine which expression is equivalent to \( 5x^2 + 10x + 15 \) using the Distributive Property, we can factor out the common factor of 5 from each term in the expression:
Starting with:
\[
5x^2 + 10x + 15
\]
Factoring out 5 gives us:
\[
5(x^2 + 2x + 3)
\]
Now let's look at the answer choices:
1. \( 5(x^2 + 2x + 3) \) - This is correct, as it matches what we factored.
2. \( 5(x^2 + 10x + 3) \) - This is incorrect.
3. \( 5(x^2 + 10x + 15) \) - This is incorrect.
4. \( x(5^x + 10 + 15) \) - This is incorrect.
Therefore, the expression that is equivalent to \( 5x^2 + 10x + 15 \) is:
**5(x^2 + 2x + 3)**
Starting with:
\[
5x^2 + 10x + 15
\]
Factoring out 5 gives us:
\[
5(x^2 + 2x + 3)
\]
Now let's look at the answer choices:
1. \( 5(x^2 + 2x + 3) \) - This is correct, as it matches what we factored.
2. \( 5(x^2 + 10x + 3) \) - This is incorrect.
3. \( 5(x^2 + 10x + 15) \) - This is incorrect.
4. \( x(5^x + 10 + 15) \) - This is incorrect.
Therefore, the expression that is equivalent to \( 5x^2 + 10x + 15 \) is:
**5(x^2 + 2x + 3)**