Question

which expression is equivalent to $x^6 - 9$?$\bigcirc\\ (x^3)^2 - 3^3LXB0\bigcirc\\ (x^3)^3 - 3^2$completethis polynomial is an example of a$\boldsymbol{\lozenge}$.

Explanation:

Step1: Simplify $x^6$ using exponent rule

Recall $(a^m)^n = a^{mn}$. So $x^6=(x^3)^2$.

Step2: Rewrite 9 as a square

$9 = 3^2$.

Step3: Match to difference of squares

The original expression $x^6 - 9$ becomes $(x^3)^2 - 3^2$, which is a difference of two squares.

Answer:

1. Equivalent expression: $(x^3)^2 - 3^2$
2. Polynomial type: difference of two squares