Question

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

Answer 1

Answer:

A and C

Step-by-step explanation:

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

Simplify each answer choice to find the expression which simplifies to $\frac{2}{x^6-y^6}$.

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.