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Answer:
Here's how to find the product:
1. Expand the Square:
- (x + 2y + 3)² means (x + 2y + 3) multiplied by itself:
(x + 2y + 3)(x + 2y + 3)
2. Use the Distributive Property (FOIL-like approach):
- Multiply each term in the first set of parentheses by each term in the second set:
- x * x = x²
- x * 2y = 2xy
- x * 3 = 3x
- 2y * x = 2xy
- 2y * 2y = 4y²
- 2y * 3 = 6y
- 3 * x = 3x
- 3 * 2y = 6y
- 3 * 3 = 9
3. Combine Like Terms:
- x² + 2xy + 3x + 2xy + 4y² + 6y + 3x + 6y + 9
- x² + 4xy + 6x + 4y² + 12y + 9
4. Multiply by 2:
- 2(x² + 4xy + 6x + 4y² + 12y + 9)
- 2x² + 8xy + 12x + 8y² + 24y + 18
Therefore, the product of 2(x + 2y + 3)² is 2x² + 8xy + 12x + 8y² + 24y + 18