factor this expression. check your work. 39. the total area of a cylind…
$2\pi r(r + h)$
Question
factor this expression. check your work.
- the total area of a cylinder is calculated by adding $2\\pi rh$ to $2\\pi r^{2}$.
Solution Steps
-
Understand the question
factor this expression. check your work.
- the total area of a cylinder is calculated by adding $2\\pi rh$ to $2\\pi r^{2}$.
-
Explanation
Step1: Identify common factor
The terms $2\pi r^2$ and $2\pi r h$ share the common factor $2\pi r$.
Step2: Factor out the common term
Factor $2\pi r$ from each term:
$2\pi r^2 + 2\pi r h = 2\pi r(r + h)$Step3: Verify by expanding
Multiply the factored form to check:
$2\pi r(r + h) = 2\pi r \cdot r + 2\pi r \cdot h = 2\pi r^2 + 2\pi r h$
This matches the original expression, confirming the factorization is correct. -
Final answer
$2\pi r(r + h)$
Answer
Explanation
Step1: Identify common factor
The terms $2\pi r^2$ and $2\pi r h$ share the common factor $2\pi r$.
Step2: Factor out the common term
Factor $2\pi r$ from each term:
$2\pi r^2 + 2\pi r h = 2\pi r(r + h)$
Step3: Verify by expanding
Multiply the factored form to check:
$2\pi r(r + h) = 2\pi r \cdot r + 2\pi r \cdot h = 2\pi r^2 + 2\pi r h$
This matches the original expression, confirming the factorization is correct.
Answer
$2\pi r(r + h)$
Question Image
Click to enlargeQuestion Analysis
Subject
mathematics
Sub Subject
geometry
Education Level
high school
Difficulty
unspecified
Question Type
calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T20:31:31
OCR Text
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factor this expression. check your work.
39. the total area of a cylinder is calculated by adding $2\\pi rh$ to $2\\pi r^{2}$.
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