Question
Factor completely. \( 25+10 b+b^{2} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 25+10 b+b^{2}=\square \) (Factor completely.) B. The trinomial is not factorable.
Ask by Salazar Ball. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 25 + 10b + b² = (b + 5)² \)
Solution
To factor the expression 25 + 10b + b², first rewrite it in standard form as b² + 10b + 25. Notice that this trinomial is a perfect square because:
1. The square of b is b².
2. The square of 5 is 25.
3. The middle term, 10b, is twice the product of b and 5 (2·b·5 = 10b).
Thus, b² + 10b + 25 factors as (b + 5)².
The correct answer is:
A. 25 + 10b + b² = (b + 5)².
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
First additional information: To factor the expression \( 25 + 10b + b^2 \), we can rearrange it in standard form to get \( b^2 + 10b + 25 \). This trinomial is a perfect square, as it can be expressed as \( (b + 5)^2 \). The middle term, \( 10b \), is twice the product of the square root of the first term (\( b \)) and the square root of the last term (\( 5 \)). Second additional information: So, we can conclude that \( 25 + 10b + b^2 = (b + 5)(b + 5) = (b + 5)^2 \). This neat little trick of recognizing perfect squares can save time and help avoid mistakes when trying to factor more complicated expressions later on.
