Question

Which of the following expressions are equivalent to 2/x^6-y^6? Choose all that apply.

Answer 1

a and c

Explanation:

Answer 2

A and C

Explanation:

Equivalent expressions are expression which when simplified to lowest terms are equal.

Simplify each answer choice to find the expression which simplifies to
`(2)/(x^6-y^6)`.

A. Multiply the exponents 3*2 = 6. This is equal.

B. Multiply numerators and denominators. Here the numerator will be 1*1 = 1. It does not equal 2 in the numerator.

C. Here the numerator does equal 2. The denominator multiplies to
`(x^3 - y^3)(x^3+y^3)\\x^6 -x^3y^3 + x^3y^3 -y^6\\x^6 - y^6`

This is equal.

D. The denominator will have three terms here when simplified. This will not be equal.