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Find the product
2
(x + 2y + 3)²


Sagot :

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