Q. \( (x+2)^3 \)
Answer
Use the binomial expansion:
\[
(x+2)^3=x^3+3x^2(2)+3x(2^2)+2^3
\]
\[
(x+2)^3=x^3+6x^2+12x+8
\]
Detailed Explanation
We want to expand the expression \( (x+2)^3 \).
Step 1: Use the binomial expansion rule
For any terms \( (a+b)^3 \), the expansion is:
\[
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
\]
Here, we identify \( a = x \) and \( b = 2 \).
Step 2: Compute each part of the expansion
Term 1: \( a^3 = x^3 \)
Term 2: \( 3a^2b = 3x^2(2) \)
\[
3x^2(2) = 6x^2
\]
Term 3: \( 3ab^2 = 3x(2^2) \)
\[
2^2 = 4
\]
So:
\[
3x(4) = 12x
\]
Term 4: \( b^3 = 2^3 \)
\[
2^3 = 8
\]
Step 3: Add all terms together
\[
(x+2)^3 = x^3 + 6x^2 + 12x + 8
\]
Final Answer:
\[
(x+2)^3 = x^3 + 6x^2 + 12x + 8
\]
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Algebra FAQ
Expand \( (x+2)^3 \).
\( (x+2)^3=x^3+6x^2+12x+8 \).
What is the binomial theorem formula for \( (a+b)^3 \)?
\( (a+b)^3=a^3+3a^2b+3ab^2+b^3 \).
How do you expand \( (x+2)^3 \) using \( (x+2)(x+2)(x+2) \)?
Multiply stepwise: first \( (x+2)^2=x^2+4x+4 \), then \( (x^2+4x+4)(x+2)=x^3+6x^2+12x+8 \).
List the coefficients of \( (x+2)^3=x^3+6x^2+12x+8 \).
Coefficients are \(1\) for \(x^3\), \(6\) for \(x^2\), \(12\) for \(x\), and \(8\) constant.
Evaluate \( (x+2)^3 \) when \(x=-1\).
\( (-1+2)^3=1^3=1 \).
Evaluate \( (x+2)^3 \) when \(x=0\).
\( (0+2)^3=2^3=8 \).
Use math AI to solve (x+2)^3.
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