`{:("Column" A ,, "Column" B), ((3x^(2) - 5)- (2x^(2) - 5 + y^(2)) ,, (a) x^(2) + xy + y^(2)) , (9x^(2) - 16y^(2) ,, (b) 2) , ((x^(3) - y^(3))/(x-y) ,, (c) (9x + 16y) (9x - 16y)) , ("The degree of " (x + 2) (x+3) ,, (d) x^(2) - y^(2)) , (,, (e) 1) , (,, (f) (3x + 4y) (3x - 4y)):}`

Explanation

To solve the problem, we need to match the expressions from Column A with the corresponding expressions in Column B. Let's go through each expression step by step.

### Step 1: Simplifying the first expression
**Expression:** \( (3x^2 - 5) - (2x^2 - 5 + y^2) \)

1. Distribute the negative sign:
\[ 3x^2 - 5 - 2x^2 + 5 - y^2 \]

2. Combine like terms:
\[ (3x^2 - 2x^2) + (-5 + 5) - y^2 = x^2 - y^2 \]

**Match:** This matches with option (d) \( x^2 - y^2 \).

### Step 2: Simplifying the second expression
**Expression:** \( 9x^2 - 16y^2 \)

1. Recognize this as a difference of squares:
\[ 9x^2 - (4y)^2 \]

2. Apply the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \):
\[ (3x - 4y)(3x + 4y) \]

**Match:** This matches with option (c) \( (9x + 16y)(9x - 16y) \).

### Step 3: Simplifying the third expression
**Expression:** \( \frac{x^3 - y^3}{x - y} \)

1. Recognize this as a factorization of the difference of cubes:
\[ x^3 - y^3 = (x - y)(x^2 + xy + y^2) \]

2. Cancel \( (x - y) \) from the numerator and denominator:
\[ x^2 + xy + y^2 \]

**Match:** This matches with option (a) \( x^2 + xy + y^2 \).

### Step 4: Finding the degree of the polynomial
**Expression:** \( (x + 2)(x + 3) \)

1. Expand the expression:
\[ x^2 + 3x + 2x + 6 = x^2 + 5x + 6 \]

2. Determine the degree:
- The highest power of \( x \) is \( 2 \).

**Match:** This matches with option (b) \( 2 \).

### Step 5: Finalizing the matches
- The first expression matches with (d).
- The second expression matches with (c).
- The third expression matches with (a).
- The fourth expression matches with (b).

### Summary of Matches:
1. \( (3x^2 - 5) - (2x^2 - 5 + y^2) \) matches with (d) \( x^2 - y^2 \).
2. \( 9x^2 - 16y^2 \) matches with (c) \( (9x + 16y)(9x - 16y) \).
3. \( \frac{x^3 - y^3}{x - y} \) matches with (a) \( x^2 + xy + y^2 \).
4. Degree of \( (x + 2)(x + 3) \) matches with (b) \( 2 \).