Explanation:

Let’s break this down step by step:

- You’re told: x³ - y³ = 112 and x - y = 4.

- Remember this formula: x³ - y³ = (x - y)(x² + xy + y²). So, plugging in, 112 = 4(x² + xy + y²).

- That gives us: x² + xy + y² = 28.

- Also, x² + y² = (x - y)² + 2xy ? x² + y² = 16 + 2xy.

- Now, from earlier: x² + xy + y² = 28.

- But x² + y² = ? So, rearrange: (x² + y²) + xy = 28, meaning x² + y² = 28 - xy.

- Substitute x² + y² from the previous line into this to get:

16 + 2xy = 28 - xy ? 3xy = 12 ? xy = 4.

- Substitute xy = 4 back in: x² + y² = 16 + 2×4 = 24.

Now, look at the options:

- 1: 16 2: 20 3: 24 4: 28

So, the correct answer is Option 3: 24

Here’s what matters:

- We used the cubic factoring identity.

- The rest is just plugging values into basic algebra.

- 24 is the number that checks out; the other options are just there to distract you.

You got it right!