Final answer:
The shortcut factoring techniques for the expressions are provided along with their respective factorizations.
Step-by-step explanation:
The shortcut factoring techniques for the given expressions are as follows:
a.) 9x² - y²: This expression requires the Difference of Perfect Squares technique. It can be factored as (3x + y)(3x - y).
b.) 8x³-1: This expression requires the Difference of Perfect Cubes technique. It can be factored as (2x - 1)(4x² + 2x + 1).
c.) 8³ + 125t⁶: This expression requires the Sum of Perfect Cubes technique. It can be factored as (2 + 5t²)(4 - 4t² + 5t⁴).
Learn more about Factoring techniques for algebraic expressions