Question

1. which pair of expressions is equivalent?

a (7x + 3) and (3x + 7)
b (x + x + x) and (x^3)
c (4(y + 2)) and (4y + 8)
d (5(z - 1)) and (5z - 5)

Explanation:

To solve this, we analyze each option by simplifying or comparing the expressions:

Option A:

First expression: \(7x + 3\)
Second expression: \(3x + 7\)
These are not equivalent (coefficients of \(x\) and constants differ).

Option B:

First expression: \(x + x + x = 3x\)
Second expression: \(x^3\) (which is \(x \times x \times x\), not \(3x\)).
Not equivalent.

Option C:

First expression: \(4(y + 2) = 4y + 8\) (by distributive property: \(4 \times y + 4 \times 2 = 4y + 8\))
Second expression: \(4y + 8\)
These are identical (equivalent).

Option D:

First expression: \(5(z - 1) = 5z - 5\) (distributive property: \(5 \times z - 5 \times 1 = 5z - 5\))
Second expression: \(5z - 5z = 0\)
Not equivalent.

Answer:

C. \(4(y + 2)\) and \(4y + 8\)