Question

Match the difference of squares with its factored form.

A. 9x^2 - 121
B. 36^2 - 25
C. X^2 - 196

A. (6x + 5) (6x - 5)
B. (X + 14) (X - 14)
C. (3x + 11) (3x - 11)

Answer 1

To match the difference of squares with its factored form, we first need to recall the format for factoring a difference of squares, which is:

\[ a^2 - b^2 = (a + b)(a - b) \]

Now let's analyze each expression:

**A. \( 9x^2 - 121 \)**
Here, \( 9x^2 \) can be expressed as \( (3x)^2 \) and \( 121 \) can be expressed as \( 11^2 \).
Therefore, the difference of squares can be factored as:
\[ (3x + 11)(3x - 11) \]

So, A matches with **C. (3x + 11) (3x - 11)**.

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**B. \( 36^2 - 25 \)**
Here, \( 36^2 \) is simply \( 36^2 \) and \( 25 \) is \( 5^2 \).
So, the difference of squares can be factored as:
\[ (36 + 5)(36 - 5) = (41)(31) \]
However, we do not have a matching factorization given, as it's likely we should represent it symbolically. It seems this one wasn’t linked correctly to any provided forms. We can list it independently or consider it if a better representation is provided.

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**C. \( X^2 - 196 \)**
Here, \( X^2 \) is already \( X^2 \) and \( 196 \) can be expressed as \( 14^2 \).
Therefore, the difference of squares can be factored as:
\[ (X + 14)(X - 14) \]

So, C matches with **B. (X + 14) (X - 14)**.

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To summarize the correct matches:

- A (9x^2 - 121) matches with C ((3x + 11)(3x - 11))
- B (36^2 - 25) doesn’t match any provided options straightforwardly but factors to (41)(31)
- C (X^2 - 196) matches with B ((X + 14)(X - 14))