Find Expressions Equal to 6x^2+8xy: Comparing Algebraic Forms

To solve this problem, we'll simplify each expression and compare it to the given expression $6x^2 + 8xy$.

• Step 1: Expand and simplify each option.
• Step 2: Compare each result with $6x^2 + 8xy$.

Let's address each expression:

Option 1: $-2(-3x^2 - 4xy)$

Apply distribution:
$-2 \times -3x^2 = 6x^2$ and $-2 \times -4xy = 8xy$
This simplifies to $6x^2 + 8xy$.

Option 2: $2(3x^2 + 4xy)$

Apply distribution:
$2 \times 3x^2 = 6x^2$ and $2 \times 4xy = 8xy$
This also simplifies to $6x^2 + 8xy$.

Option 3: $2x(3x + 4y)$

Expand via distribution:
$2x \times 3x = 6x^2$ and $2x \times 4y = 8xy$
This simplifies to $6x^2 + 8xy$.

Option 4: $2y(\frac{3x^2}{y} + 4x)$

Inside the parentheses, distribute $2y$:
$2y \times \frac{3x^2}{y} = 6x^2$ and $2y \times 4x = 8xy$
This simplifies to $6x^2 + 8xy$.

Therefore, each expression, when simplified, is equal to the original expression $6x^2 + 8xy$. Hence, all expressions are equal.