Q. \((x+2)^2\)

Q: What is the first term when expanding (x+2)^2 ?

The first (highest-degree) term is x^2 .

Q: Find the middle term coefficient in (x+2)^2 .

The middle term is 4x , so the coefficient of x is 4 .

Q: Rewrite (x+2)^2 in standard polynomial form.

In standard form, (x+2)^2 = x^2 + 4x + 4 .

Q: Solve (x+2)^2 = 0 .

x+2=0 \Rightarrow x=-2 (double root).

Answer

To expand \((x+2)^2\), use \((a+b)^2=a^2+2ab+b^2\). Here \(a=x\) and \(b=2\).

\[
(x+2)^2 = x^2 + 2\cdot x \cdot 2 + 2^2 = x^2 + 4x + 4
\]

Detailed Explanation

To simplify \(\left(x+2\right)^2\), we use the binomial square rule:

\[
\left(a+b\right)^2 = a^2 + 2ab + b^2
\]

Here we identify \(a = x\) and \(b = 2\). Substitute into the rule:

\[
\left(x+2\right)^2 = x^2 + 2\cdot x \cdot 2 + 2^2
\]

Now compute each term:

\[
x^2 \text{ stays as } x^2
\]

Second term:

\[
2\cdot x \cdot 2 = 4x
\]

Third term:

\[
2^2 = 4
\]

Combine the terms:

\[
\left(x+2\right)^2 = x^2 + 4x + 4
\]

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Algebra FAQ

Expand \( (x+2)^2 \).

\( (x+2)^2 = x^2 + 4x + 4 \).

What is the first term when expanding \( (x+2)^2 \)?

The first (highest-degree) term is \( x^2 \).

Find the middle term coefficient in \( (x+2)^2 \).

The middle term is \( 4x \), so the coefficient of \( x \) is \( 4 \).

What constant term results from \( (x+2)^2 \)?

The constant term is \( 4 \).

Derive \( (x+2)^2 \) using FOIL.

\( (x+2)(x+2) = x\cdot x + x\cdot 2 + 2\cdot x + 2\cdot 2 = x^2 + 4x + 4 \).

Rewrite \( (x+2)^2 \) in standard polynomial form.

In standard form, \( (x+2)^2 = x^2 + 4x + 4 \).

Solve \( (x+2)^2 = 0 \).

\( x+2=0 \Rightarrow x=-2 \) (double root).

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