Question

1. select one of the expression that is equivalent to 32a+12b+2a

a. 2(16a+6b+2a)
b. 8b+4b+3a - a+12a - 30a
c. 2(17a+6b)
d. 2(a+b)+32a+6b

Explanation:

Step1: Simplify the original expression

The original expression is \(32a + 12b+2a\). Combine like terms: \(32a+2a = 34a\), so the original expression simplifies to \(34a + 12b\).

Step2: Analyze Option A

Simplify \(2(16a + 6b+2a)\). First, combine like terms inside the parentheses: \(16a + 2a=18a\), so we have \(2(18a + 6b)=36a+12b\). This is not equal to \(34a + 12b\), so A is incorrect.

Step3: Analyze Option B

Simplify \(8b + 4b+3a - a+12a - 30a\). Combine like terms for \(b\): \(8b + 4b = 12b\). Combine like terms for \(a\): \(3a - a+12a - 30a=(3 - 1+12 - 30)a=(-16)a\). So the expression is \(-16a + 12b\), which is not equal to \(34a + 12b\), so B is incorrect.

Step4: Analyze Option C

Simplify \(2(17a+6b)\). Using the distributive property, we get \(2\times17a+2\times6b = 34a+12b\), which matches the simplified original expression. Let's check Option D for completeness.

Step5: Analyze Option D

Simplify \(2(a + b)+32a+6b\). Distribute the 2: \(2a+2b + 32a+6b\). Combine like terms: \(2a+32a=34a\), \(2b + 6b = 8b\). So the expression is \(34a+8b\), which is not equal to \(34a + 12b\), so D is incorrect.

Answer:

C. \(2(17a + 6b)\)