Question

factor the following trinomial.

\\16x^2 + 72x + 81\\

\\((?x + \quad)^2\\)

Explanation:

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<reasoning>

Identify the perfect square terms

Using the Perfect Square Trinomials knowledge point
\[

$$\begin{aligned} 16x^2 &= (4x)^2 \\ 81 &= 9^2 \end{aligned}$$

\]

Verify the middle term

Using the Perfect Square Trinomials knowledge point
\[
2 \cdot (4x) \cdot 9 = 72x
\]

Write the factored form

Using the Perfect Square Trinomials knowledge point
\[
16x^2 + 72x + 81 = (4x + 9)^2
\]
</reasoning>

<answer>
Factor the following trinomial.

\(16x^2 + 72x + 81\)

(<blank>4</blank>\(x +\) <blank>9</blank>)\(^2\)
</answer>

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"Mathematics",
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"Perfect Square Trinomials"
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Answer:

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<reasoning>

Identify the perfect square terms

Using the Perfect Square Trinomials knowledge point
\[

$$\begin{aligned} 16x^2 &= (4x)^2 \\ 81 &= 9^2 \end{aligned}$$

\]

Verify the middle term

Using the Perfect Square Trinomials knowledge point
\[
2 \cdot (4x) \cdot 9 = 72x
\]

Write the factored form

Using the Perfect Square Trinomials knowledge point
\[
16x^2 + 72x + 81 = (4x + 9)^2
\]
</reasoning>

<answer>
Factor the following trinomial.

\(16x^2 + 72x + 81\)

(<blank>4</blank>\(x +\) <blank>9</blank>)\(^2\)
</answer>

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