# Which of the following equations is NOT equivalent to…

## Solution:

To solve this question, we start by FOILing the right hand side of the given equation.

10y^2 = (x+2)(x-2)

10y^2 = x^2 – 4

We will manipulate each of the answer choices to see if it equals 10y^2 = x^2 – 4. Let’s start with A.

**A) 30y^2 =3x^2 – 12**

If we divide this entire equation by 3 we are left with:

10y^2 = x^2 – 4

Answer choice A is not correct.

**B) 20y^2 = (2x-4)(x+2)**

FOILing (2x-4)(x+2) we get:

20y^2 = 2x^2 – 8

If we divide this entire equation by 2 we obtain:

10y^2 = x^2 – 4

Answer choice B is not correct.

**C) 10y^2 + 4 = x^2**

If we subtract 4 from the both sides of the equation, we obtain:

10y^2 = x^2 – 4

Answer choice C is not correct.

**D) 5y^2 = x^2 – 2**

We should notice that no matter how we try to manipulate 5y^2 = x^2 – 2, it will never be equal to 10y^2 = x^2 – 4. For example, if we multiply both sides of 5y^2 = x^2 – 2 by 2, we will have 10y^2 = 2x^2 – 4. However, that is not the same as 10y^2 = x^2 – 4.

Answer D is correct.

To be certain, we should also test answer E.

**E) y^2 = (x^2 – 4)/10**

If we multiply the entire equation by 10 we obtain:

10y^2 = x^2 – 4

Answer choice E is not correct.

**Answer: D**