Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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
Transcribed Image Text:**Transcription for Educational Website:**
---
**Solve for x**
\((x+3)^2\)
- ○ \(x^2 + 3x + 2\)
- ○ \(2x^2 + 3x + 2\)
- ○ \(x^2 + 6x + 2\)
- ○ \(x^2 + 6x + 9\)
---
**Explanation:**
You are asked to expand the expression \((x+3)^2\). To do this, apply the algebraic identity \((a+b)^2 = a^2 + 2ab + b^2\). In this case, \(a = x\) and \(b = 3\).
Calculating:
- \(a^2 = x^2\)
- \(2ab = 2 \cdot x \cdot 3 = 6x\)
- \(b^2 = 3^2 = 9\)
So, \((x+3)^2 = x^2 + 6x + 9\).
Therefore, the correct option is the last one: \(x^2 + 6x + 9\).
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