
                ### Instruction: help me answer this question Prove that the expression (x + y) {mx2 + y2k (x – y)} is a factor of the expression x2k . x2 – y2k . y2, think step by step
                ### Assistant: N/A , The answer is We can prove this by expanding the expression and showing that it can be written in the form (x + y) times some other expression.
First, we add and subtract y2k in the expression x2k . x2 – y2k . y2 to get x2 (x2k – y2k + y2k) – y2k. y2. From equation (1), we get x2 {m (x + y) + y2k} – y2k. y2. By multiplying the terms, we get m (x + y) x2 + y2k. x2 – y2k. y2. Taking out the common terms, we get m (x + y) x2 + y2k (x – y). Expanding using the formula, we get m (x + y) x2 + y2k (x + y) (x – y). So, we get (x + y) {mx2 + y2k (x – y)}
