factor: $8 + x^3$ a $(2+x)(4-2x+x^2)$ b $(2+x)^3$ c $(2-x)(4+2x+x^2)$ d…
A. $(2+x)(4-2x+x^2)$
Aufgabe
factor: $8 + x^3$
a $(2+x)(4-2x+x^2)$
b $(2+x)^3$
c $(2-x)(4+2x+x^2)$
d $(2+x)(4+x^2)$
$a^2 + 2ab + b^2=(a+b)^2$
$a^2 - 2ab + b^2=(a-b)^2$
$a^3 + b^3=(a+b)(a^2 - ab + b^2)$
$a^3 - b^3=(a-b)(a^2 + ab + b^2)$
Lösungsschritte
-
Understand the question
factor: $8 + x^3$
a $(2+x)(4-2x+x^2)$
b $(2+x)^3$
c $(2-x)(4+2x+x^2)$
d $(2+x)(4+x^2)$
$a^2 + 2ab + b^2=(a+b)^2$
$a^2 - 2ab + b^2=(a-b)^2$
$a^3 + b^3=(a+b)(a^2 - ab + b^2)$
$a^3 - b^3=(a-b)(a^2 + ab + b^2)$ -
Explanation
Step1: Identify sum of cubes
$8+x^3 = 2^3 + x^3$
Step2: Apply sum of cubes formula
Use $a^3+b^3=(a+b)(a^2-ab+b^2)$ where $a=2, b=x$:
$\begin{align*}
2^3+x^3&=(2+x)(2^2 - 2x + x^2)\\
&=(2+x)(4-2x+x^2)
\end{align*}$ -
Final answer
A. $(2+x)(4-2x+x^2)$
Antwort
Explanation
Step1: Identify sum of cubes
$8+x^3 = 2^3 + x^3$
Step2: Apply sum of cubes formula
Use $a^3+b^3=(a+b)(a^2-ab+b^2)$ where $a=2, b=x$:
$\begin{align*}
2^3+x^3&=(2+x)(2^2 - 2x + x^2)\\
&=(2+x)(4-2x+x^2)
\end{align*}$
Answer
A. $(2+x)(4-2x+x^2)$
Question Image
Click to enlargeQuestion Analysis
Subject
mathematics
Sub Subject
algebra
Education Level
high school
Difficulty
unspecified
Question Type
multiple choice, calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T19:50:19
OCR Text
Show OCR extraction
factor: $8 + x^3$ a $(2+x)(4-2x+x^2)$ b $(2+x)^3$ c $(2-x)(4+2x+x^2)$ d $(2+x)(4+x^2)$ $a^2 + 2ab + b^2=(a+b)^2$ $a^2 - 2ab + b^2=(a-b)^2$ $a^3 + b^3=(a+b)(a^2 - ab + b^2)$ $a^3 - b^3=(a-b)(a^2 + ab + b^2)$
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