Which expression is equivalent to 30(12x−2)+40(34y−4)

Question

(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

Answer 1

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.