Rút gọn biểu thức

To simplify the expressions you've provided, let’s go through each part individually.

### a.
\[ B = x(x + 2y)^3 - y(xy + 2x)^3 \]

You would want to expand both terms and then combine like terms.

### b.
\[ C = x^4 + (2x + y)^4 + y^4 \]

You can expand \((2x + y)^4\) using the binomial theorem, then combine it with the other terms.

### c.
\[ D = -a^4 + b^4 + 2(a^2b^2 + b^4 + c^2a^2) \]

This is a direct polynomial expression; calculation involves rearranging and simplifying.

### d.
\[ A = (a + b + c - a)^2 + b(c + a - 6)^2 + c(a + b - c)^2 + (b + c - a)(c + a - b)(a + b + c) \]

To simplify, expand all squared terms and combine like terms.

### General Approach:
1. **Expand** the terms using algebraic identities.
2. **Combine like terms** while keeping an eye on the coefficients.
3. **Factor** where possible to see if it can be reduced.

If you want help with a specific part, let me know!