what is the factorization of 81a^6 - 100?\n(9a^2 - 10)(9a^3 + 10)\n(9a^2 - 10)(9a^3 - 10)\n(9a^3 - 10)(9a^3…
what is the factorization of 81a^6 - 100?\n(9a^2 - 10)(9a^3 + 10)\n(9a^2 - 10)(9a^3 - 10)\n(9a^3 - 10)(9a^3 + 10)\n(9a^3 - 10)(9a^3 - 10)
Answer
Answer:
C. $(9a^{3}-10)(9a^{3}+10)$
Explanation:
Step1: Recognize difference - of - squares formula
The formula for the difference of squares is $x^{2}-y^{2}=(x - y)(x + y)$.
Step2: Rewrite the given expression
We can rewrite $81a^{6}-100$ as $(9a^{3})^{2}-10^{2}$, where $x = 9a^{3}$ and $y = 10$.
Step3: Apply the formula
Using the difference - of - squares formula, $(9a^{3})^{2}-10^{2}=(9a^{3}-10)(9a^{3}+10)$.