Determine whether the following expressions are equivalent:

Question

94a+28
94
𝑎
+
28
and 108a−14(a−2)
108
𝑎
−
14
(
𝑎
−
2
)
.

(1 point)
Responses

Yes, because 108a−14(a−2)
108
𝑎
−
14
(
𝑎
−
2
)
simplifies to 94a+28
94
𝑎
+
28
.
Yes, because 108 a minus 14 left parenthesis a minus 2 right parenthesis simplifies to 94 a plus 28 .

No, because 108a−14(a−2)
108
𝑎
−
14
(
𝑎
−
2
)
simplifies to 94a−28
94
𝑎
−
28
.
No, because 108 a minus 14 left parenthesis a minus 2 right parenthesis simplifies to 94 a minus 28 .

Yes, because 108a−14(a−2)
108
𝑎
−
14
(
𝑎
−
2
)
simplifies to 28−94a
28
−
94
𝑎
.
Yes, because 108 a minus 14 left parenthesis a minus 2 right parenthesis simplifies to 28 minus 94 a .

No, because 108a−14(a−2)
108
𝑎
−
14
(
𝑎
−
2
)
simplifies to 136a−14
136
𝑎
−
14
.

Answer 1

To determine if the expressions \( 94a + 28 \) and \( 108a - 14(a - 2) \) are equivalent, we need to simplify the second expression.

Starting with \( 108a - 14(a - 2) \):

1. Distribute the \( -14 \): \[ 108a - 14a + 28 \] This is because \(-14(a - 2) = -14a + 28\).

2. Combine like terms: \[ (108a - 14a) + 28 = 94a + 28 \]

Now we have simplified \( 108a - 14(a - 2) \) to \( 94a + 28 \), which is exactly the first expression.

Therefore, the answer is:

Yes, because \( 108a - 14(a - 2) \) simplifies to \( 94a + 28 \).