To determine which expressions are equivalent to \( 12x + 36y \), we need to check if these expressions simplify to the original expression when expanded.
Let's evaluate each given expression one by one:
1. \( 9(3x + 4y) \)
- Expanding this: \( 9 \cdot 3x + 9 \cdot 4y = 27x + 36y \)
- This is not equivalent to \( 12x + 36y \).
2. \( 2(6x + 24y) \)
- Expanding this: \( 2 \cdot 6x + 2 \cdot 24y = 12x + 48y \)
- This is not equivalent to \( 12x + 36y \).
3. \( 6(2x + 6y) \)
- Expanding this: \( 6 \cdot 2x + 6 \cdot 6y = 12x + 36y \)
- This is equivalent to \( 12x + 36y \).
4. \( 3(4x + 12y) \)
- Expanding this: \( 3 \cdot 4x + 3 \cdot 12y = 12x + 36y \)
- This is equivalent to \( 12x + 36y \).
5. \( 12(x + 3y) \)
- Expanding this: \( 12 \cdot x + 12 \cdot 3y = 12x + 36y \)
- This is equivalent to \( 12x + 36y \).
6. \( 4(3x + 9y) \)
- Expanding this: \( 4 \cdot 3x + 4 \cdot 9y = 12x + 36y \)
- This is equivalent to \( 12x + 36y \).
Therefore, the expressions that are equivalent to \( 12x + 36y \) are:
- \( 6(2x + 6y) \)
- \( 3(4x + 12y) \)
- \( 12(x + 3y) \)
- \( 4(3x + 9y) \)
which expressions are equivalent to 12x + 36y choose all that apply.
9(3x+4y), 2(6x+24y), 6(2x+6y)
, 3(4x+12y), 12(x+3y) and 4(3x+9y)
1 answer
1 answer