Question

which are perfect square trinomials? select two options.

\\(x^2 - 9\\)

\\(x^2 - 100\\)

\\(x^2 - 4x + 4\\)

\\(x^2 + 10x + 25\\)

\\(x^2 + 15x + 36\\)

Explanation:

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<reasoning>

Define perfect square trinomials

Using the Perfect Square Trinomial knowledge point
\[
(a \pm b)^2 = a^2 \pm 2ab + b^2
\]

Analyze binomial options

Using the Perfect Square Trinomial knowledge point
\[

$$\begin{aligned} &x^2 - 9 = (x - 3)(x + 3) \quad \text{(Difference of Squares)} \\ &x^2 - 100 = (x - 10)(x + 10) \quad \text{(Difference of Squares)} \end{aligned}$$

\]

Analyze trinomial options

Using the Perfect Square Trinomial knowledge point
\[

$$\begin{aligned} &x^2 - 4x + 4 = x^2 - 2(x)(2) + 2^2 = (x - 2)^2 \\ &x^2 + 10x + 25 = x^2 + 2(x)(5) + 5^2 = (x + 5)^2 \\ &x^2 + 15x + 36 = (x + 12)(x + 3) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x^2 - 9\)</mcq-option>
<mcq-option>\(x^2 - 100\)</mcq-option>
<mcq-correct>\(x^2 - 4x + 4\)</mcq-correct>
<mcq-correct>\(x^2 + 10x + 25\)</mcq-correct>
<mcq-option>\(x^2 + 15x + 36\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Define perfect square trinomials

Using the Perfect Square Trinomial knowledge point
\[
(a \pm b)^2 = a^2 \pm 2ab + b^2
\]

Analyze binomial options

Using the Perfect Square Trinomial knowledge point
\[

$$\begin{aligned} &x^2 - 9 = (x - 3)(x + 3) \quad \text{(Difference of Squares)} \\ &x^2 - 100 = (x - 10)(x + 10) \quad \text{(Difference of Squares)} \end{aligned}$$

\]

Analyze trinomial options

Using the Perfect Square Trinomial knowledge point
\[

$$\begin{aligned} &x^2 - 4x + 4 = x^2 - 2(x)(2) + 2^2 = (x - 2)^2 \\ &x^2 + 10x + 25 = x^2 + 2(x)(5) + 5^2 = (x + 5)^2 \\ &x^2 + 15x + 36 = (x + 12)(x + 3) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x^2 - 9\)</mcq-option>
<mcq-option>\(x^2 - 100\)</mcq-option>
<mcq-correct>\(x^2 - 4x + 4\)</mcq-correct>
<mcq-correct>\(x^2 + 10x + 25\)</mcq-correct>
<mcq-option>\(x^2 + 15x + 36\)</mcq-option>
</answer>

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