Find the product. Assume variables represent positive real numbers.
-$$\left( m 1 / 6 + m ^ { - 1 / 6 } \right) \left( m ^ { - 1 / 6 } - m ^ { 1 / 6 } \right)$$
A) $1 - \mathrm { m } ^ { 1 / 3 } + \mathrm { m } ^ { - 1 / 3 } - \mathrm { m }$
B) $\mathrm { m } 1 / 3 - \mathrm { m } - 1 / 3$
C) $- \mathrm { m } 1 / 3 + \mathrm { m } ^ { - 1 / 3 }$
D) $\mathrm { m } - \mathrm { m } 1 / 3 + \mathrm { m } - 1 / 3 - 1$

Question

Quizplus · Accepted Answer

This is a difference of squares problem: $(a+b)(a-b) = a^2 - b^2$. Here, $a = m^{1/6}$ and $b = m^{-1/6}$. Thus, the product is $a^2 - b^2 = m^{1/3} - m^{-1/3}$, which simplifies to the expression in choice C.

Find the Product (m1/6+m−1/6)(m−1/6−m1/6)\left( m 1 / 6 + m ^ { - 1 / 6 } \right) \left( m ^ { - 1 / 6 } - m ^ { 1 / 6 } \right)(m1/6+m−1/6)(m−1/6−m1/6)

Find the Product $\left( m 1 / 6 + m ^ { - 1 / 6 } \right) \left( m ^ { - 1 / 6 } - m ^ { 1 / 6 } \right)$