Question
Factor. (If the expression is not factorable using integers, enter PRIME.) \[ r^{2}+40 r+400 \] SUBMIT ANSWER
Ask by Franklin Norris. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression factors to \( (r + 20)^2 \).
Solution
1. Given the quadratic expression:
\[
r^2 + 40r + 400
\]
2. We look for two numbers that multiply to \(400\) (the constant term) and add up to \(40\) (the coefficient of \(r\)).
3. Notice that \(20 \times 20 = 400\) and \(20 + 20 = 40\).
4. Therefore, the expression can be factored as:
\[
(r + 20)(r + 20) = (r+20)^2
\]
5. The final factored form is:
\[
(r+20)^2
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To factor the quadratic expression \( r^{2}+40r+400 \), we look for two numbers that multiply to \( 400 \) (the constant term) and add up to \( 40 \) (the coefficient of \( r \)). The numbers \( 20 \) and \( 20 \) satisfy both conditions because \( 20 \times 20 = 400 \) and \( 20 + 20 = 40 \). Thus, we can express the quadratic as: \[ (r + 20)(r + 20) \quad \text{or} \quad (r + 20)^2 \] So, the factored form is: \[ (r + 20)^2 \]
