Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( n(15r^2 + 22rs - 5s^2) \).
Solution
To simplify the expression \( n(3 r + 5 s)(5 r - s) \), we will use the distributive property (also known as the FOIL method for binomials) to expand the product of the two binomials \( (3 r + 5 s) \) and \( (5 r - s) \).
### Step 1: Expand the expression
We will multiply each term in the first binomial by each term in the second binomial:
1. **First:** \( 3r \cdot 5r = 15r^2 \)
2. **Outer:** \( 3r \cdot (-s) = -3rs \)
3. **Inner:** \( 5s \cdot 5r = 25rs \)
4. **Last:** \( 5s \cdot (-s) = -5s^2 \)
### Step 2: Combine like terms
Now, we combine the results from the expansion:
\[
15r^2 + (-3rs + 25rs) - 5s^2 = 15r^2 + 22rs - 5s^2
\]
### Step 3: Multiply by \( n \)
Now, we multiply the entire expression by \( n \):
\[
n(15r^2 + 22rs - 5s^2)
\]
### Final Result
Thus, the simplified expression is:
\[
n(15r^2 + 22rs - 5s^2)
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To solve the expression \( n(3r + 5s)(5r - s) \), we can use the distributive property to expand it. First, distribute \( (3r + 5s) \) and \( (5r - s) \): \[ (3r + 5s)(5r - s) = 3r \cdot 5r + 3r \cdot (-s) + 5s \cdot 5r + 5s \cdot (-s) \] This simplifies to: \[ 15r^2 - 3rs + 25rs - 5s^2 = 15r^2 + 22rs - 5s^2 \] Now, we multiply this result by \( n \) to get: \[ n(15r^2 + 22rs - 5s^2) \] So, the final expression is: \[ 15nr^2 + 22nrs - 5ns^2 \] That’s how we neatly expand it!
