Question

what method of factoring should first be used?
y^{10} - 1
answer
greatest common factor \t difference of perfect squares
trinomial factoring \t none of the above

Explanation:

First, check for a greatest common factor (GCF) of the terms $y^{10}$ and $1$. The GCF of $y^{10}$ and $1$ is 1, so factoring out a GCF does not simplify the expression. Next, recognize that $y^{10} = (y^5)^2$ and $1 = 1^2$, so the expression fits the form of a difference of perfect squares: $a^2 - b^2$ where $a=y^5$ and $b=1$. Trinomial factoring does not apply here as the expression is a binomial, not a trinomial.

Answer:

Difference of Perfect Squares