Problem: The expression a3−a−3a^{3}-a^{-3}a3−a−3 equals:
Answer Choices:
A. (a−1a)(a2+1+1a2)\left(a-\dfrac{1}{a}\right)\left(a^{2}+1+\dfrac{1}{a^{2}}\right)(a−a1)(a2+1+a21)
B. (1a−a)(a2−1+1a2)\left(\dfrac{1}{a}-a\right)\left(a^{2}-1+\dfrac{1}{a^{2}}\right)(a1−a)(a2−1+a21)
C. (a−1a)(a2−2+1a2)\left(a-\dfrac{1}{a}\right)\left(a^{2}-2+\dfrac{1}{a^{2}}\right)(a−a1)(a2−2+a21)
D. (1a−a)(1a2+1+a2)\left(\dfrac{1}{a}-a\right)\left(\dfrac{1}{a^{2}}+1+a^{2}\right)(a1−a)(a21+1+a2)
E. (none of these) Solution:
a3−a−3=a3−1a3=(a−1a)(a2+1+1a2)a^{3}-a^{-3}=a^{3}-\dfrac{1}{a^{3}}=\left(a-\dfrac{1}{a}\right)\left(a^{2}+1+\dfrac{1}{a^{2}}\right)a3−a−3=a3−a31=(a−a1)(a2+1+a21).