Question

Choose the THREE expressions that are equivalent to .
Responses

18 times open paren x plus 12 y close paren

6 times open paren 3 x plus 2 y close paren

3 times open paren 4 x plus 6 y close paren

10 x plus 10 y plus 5 x plus x plus 2 y plus x

9 x plus x plus 7 y plus 8 x plus 5 y

2 times open paren 6 y plus 9 x close paren

Answer 1

To determine which expressions are equivalent to \( 18(x + 12y) \), we can simplify each expression and see if they match.

1. **Expression 1:** \( 18(x + 12y) \)
- This is the original expression.

2. **Expression 2:** \( 6(3x + 2y) \)
- Distributing \( 6 \):
\[
6(3x + 2y) = 18x + 12y
\]
- This is equivalent to \( 18(x + 12y) \).

3. **Expression 3:** \( 3(4x + 6y) \)
- Distributing \( 3 \):
\[
3(4x + 6y) = 12x + 18y
\]
- This is **not** equivalent to \( 18(x + 12y) \).

4. **Expression 4:** \( 10x + 10y + 5x + x + 2y + x \)
- Combining like terms:
\[
(10x + 5x + x + x) + (10y + 2y) = 17x + 12y
\]
- This is **not** equivalent to \( 18(x + 12y) \).

5. **Expression 5:** \( 9x + x + 7y + 8x + 5y \)
- Combining like terms:
\[
(9x + x + 8x) + (7y + 5y) = 18x + 12y
\]
- This is equivalent to \( 18(x + 12y) \).

6. **Expression 6:** \( 2(6y + 9x) \)
- Distributing \( 2 \):
\[
2(6y + 9x) = 12y + 18x
\]
- This can also be rearranged to \( 18(x + 12y) \).

The equivalent expressions to \( 18(x + 12y) \) are:
- \( 18(x + 12y) \)
- \( 6(3x + 2y) \)
- \( 9x + x + 7y + 8x + 5y \)

So, the three expressions that are equivalent are:
1. \( 18(x + 12y) \)
2. \( 6(3x + 2y) \)
3. \( 9x + x + 7y + 8x + 5y \)