Asked by shhh
Which expression is equivalent to 30(12x−2)+40(34y−4)
(1 point)
Responses
45xy−220
45 x y minus 220
15x+30y−220
15 x plus 30 y minus 220
15x−30y−220
15 x minus 30 y minus 220
15x+30y−64
15 x plus 30 y minus 64
(1 point)
Responses
45xy−220
45 x y minus 220
15x+30y−220
15 x plus 30 y minus 220
15x−30y−220
15 x minus 30 y minus 220
15x+30y−64
15 x plus 30 y minus 64
Answers
Answered by
GPT-4o mini
To simplify the expression \( 30(12x - 2) + 40(34y - 4) \), we can distribute the constants through the parentheses.
1. Distributing \( 30 \) to \( (12x - 2) \):
\[
30 \cdot 12x - 30 \cdot 2 = 360x - 60
\]
2. Distributing \( 40 \) to \( (34y - 4) \):
\[
40 \cdot 34y - 40 \cdot 4 = 1360y - 160
\]
3. Now, combine the results from step 1 and step 2:
\[
(360x - 60) + (1360y - 160) = 360x + 1360y - 60 - 160
\]
\[
= 360x + 1360y - 220
\]
To express this in terms of a simplified form, we factor out common terms if possible. In this case, the expression doesn’t simplify any further; we can just rewrite it for clarity.
Therefore, the equivalent expression is:
\[
\boxed{360x + 1360y - 220}
\]
Now, let's look at the provided answer choices:
- 45xy - 220
- 15x + 30y - 220
- 15x - 30y - 220
- 15x + 30y - 64
None of the provided answer choices match the simplified expression \( 360x + 1360y - 220 \). Therefore, there may have been an error in the answer choices or the options may not reflect the correct simplification.
If you meant "45xy - 220" or others in any specific context, particularly rewriting in terms of factors, please provide further context or confirm the original expression to explore alternative interpretations.
1. Distributing \( 30 \) to \( (12x - 2) \):
\[
30 \cdot 12x - 30 \cdot 2 = 360x - 60
\]
2. Distributing \( 40 \) to \( (34y - 4) \):
\[
40 \cdot 34y - 40 \cdot 4 = 1360y - 160
\]
3. Now, combine the results from step 1 and step 2:
\[
(360x - 60) + (1360y - 160) = 360x + 1360y - 60 - 160
\]
\[
= 360x + 1360y - 220
\]
To express this in terms of a simplified form, we factor out common terms if possible. In this case, the expression doesn’t simplify any further; we can just rewrite it for clarity.
Therefore, the equivalent expression is:
\[
\boxed{360x + 1360y - 220}
\]
Now, let's look at the provided answer choices:
- 45xy - 220
- 15x + 30y - 220
- 15x - 30y - 220
- 15x + 30y - 64
None of the provided answer choices match the simplified expression \( 360x + 1360y - 220 \). Therefore, there may have been an error in the answer choices or the options may not reflect the correct simplification.
If you meant "45xy - 220" or others in any specific context, particularly rewriting in terms of factors, please provide further context or confirm the original expression to explore alternative interpretations.