Question

value: 4

match the items.

a. \\((x + 5)(x - 5)\\)
b. \\((x - 8)(x + 5)\\)
c. \\((x + 1)(x + 5)\\)
d. \\((x + 1)(x + 7)\\)

1. \\(x^2 + 6x + 5 = 0\\)
2. \\(x^2 - 25 = 0\\)
3. \\(x^2 - 3x - 40 = 0\\)
4. \\(x^2 + 8x + 7 = 0\\)

Explanation:

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<reasoning>

Expand expression a

\[
(x + 5)(x - 5) = x^2 - 25
\]

Expand expression b

\[
(x - 8)(x + 5) = x^2 + 5x - 8x - 40 = x^2 - 3x - 40
\]

Expand expression c

\[
(x + 1)(x + 5) = x^2 + 5x + x + 5 = x^2 + 6x + 5
\]

Expand expression d

\[
(x + 1)(x + 7) = x^2 + 7x + x + 7 = x^2 + 8x + 7
\]
</reasoning>

<answer>

No.	Problem	Answer
2	\(x^2 - 25 = 0\)	a
3	\(x^2 - 3x - 40 = 0\)	b
4	\(x^2 + 8x + 7 = 0\)	d

</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Expand expression a

\[
(x + 5)(x - 5) = x^2 - 25
\]

Expand expression b

\[
(x - 8)(x + 5) = x^2 + 5x - 8x - 40 = x^2 - 3x - 40
\]

Expand expression c

\[
(x + 1)(x + 5) = x^2 + 5x + x + 5 = x^2 + 6x + 5
\]

Expand expression d

\[
(x + 1)(x + 7) = x^2 + 7x + x + 7 = x^2 + 8x + 7
\]
</reasoning>

<answer>

No.	Problem	Answer
2	\(x^2 - 25 = 0\)	a
3	\(x^2 - 3x - 40 = 0\)	b
4	\(x^2 + 8x + 7 = 0\)	d

</answer>

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