Question

Let A, B, C, and D be four 4 × 4 matrices. Expand A(B + 2C)² . The correct solution is not AB² + 4ABC + 4AC²

Answer 1

To expand A(B + 2C)², distribute A to both terms inside the parentheses, square the result, and simplify the expression.

Step-by-step explanation:

To expand the expression A(B + 2C)², we need to distribute A to both terms inside the parentheses and then square the result. Let's break it down step-by-step:

1. Distribute A to B: AB
2. Distribute A to 2C: 2AC
3. Add the two terms together: AB + 2AC
4. Square the result: (AB + 2AC)²
5. Expand using the FOIL method: AB * AB + AB * 2AC + 2AC * AB + 2AC * 2AC
6. Simplify the expression: AB² + 2ABC + 2AC² + 4AC²

Therefore, the correct expansion of A(B + 2C)² is AB² + 2ABC + 4AC².