Question

Camila stated that the example below is correct but Fernando did not agree with her. Explain who is correct and why. 4x² + 8xy + 4y^2 (2x)^2+8xy+(2y)^2(2x)^2+4xy+(2y)^2(2x+2y)^2​

A) Camila is correct; the expression is simplified.
B) Fernando is correct; the expression is not simplified.
C) Both are correct; the expressions are equivalent.
D) Neither is correct; the expressions are not equivalent.

Answer 1

Neither Camila nor Fernando is correct. The expression is not simplified. The correct answer is D) Neither is correct; the expressions are not equivalent.

Step-by-step explanation:

Neither Camila nor Fernando is correct. The expression is not simplified. To simplify the expression, we need to expand the terms using the distributive property and simplify the resulting expression. Let's start:

1. Expand the first term: (2x)^2 = 4x^2
2. Expand the second term: (2y)^2 = 4y^2
3. Expand the third term: (2x+2y)^2 = (2x+2y)(2x+2y) = 4x^2 + 8xy + 4y^2

Now let's simplify the expression:

1. Combine like terms: 4x^2 + 8xy + 4y^2 + 8xy + 4xy + 4y^2
2. Simplify further: 4x^2 + 16xy + 8y^2 + 4xy + 4y^2
3. Combine like terms again: 4x^2 + 20xy + 12y^2

Therefore, the correct answer is D) Neither is correct; the expressions are not equivalent.