32x+8=?

Which algebric expression has the same value, explain method, please..

4(x+2)
8(4x+1)
4(8x+1)
8(4x+8)

Expand each of the answers. The first answer is 4x +8 which isn't the original expression. The last one is 32x + 64 which isn't the original. You try the other two.

To determine which algebraic expression has the same value as 32x+8, we need to simplify each expression and see if it results in the same outcome.

Let's simplify the given expressions one by one:

1. 4(x+2)
To simplify, we distribute the 4 to both terms inside the parentheses:
4(x+2) = 4*x + 4*2 = 4x + 8

2. 8(4x+1)
Similarly, we distribute the 8 to both terms inside the parentheses:
8(4x+1) = 8*4x + 8*1 = 32x + 8

3. 4(8x+1)
Distributing the 4 to both terms inside the parentheses:
4(8x+1) = 4*8x + 4*1 = 32x + 4

4. 8(4x+8)
Distributing the 8 to both terms inside the parentheses:
8(4x+8) = 8*4x + 8*8 = 32x + 64

Now, we can compare the simplified expressions with the original expression, which is 32x+8.

From the simplified expressions:
- 4x + 8 is the same as 32x + 8.
- 32x + 8 is the same as 32x + 8.
- 32x + 4 is different from 32x + 8.
- 32x + 64 is different from 32x + 8.

Therefore, the expression 4(x+2) has the same value as 32x+8.