1. **State the problem:** Simplify or factor the expression $10x^2 - 9$. 2. **Formula and rules:** This is a quadratic expression. We can try to factor it using the difference of squares rule if possible. The difference of squares formula is: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Intermediate work:** Rewrite the expression as: $$10x^2 - 9 = (\sqrt{10}x)^2 - 3^2$$ 4. **Apply difference of squares:** Using the formula: $$10x^2 - 9 = (\sqrt{10}x - 3)(\sqrt{10}x + 3)$$ 5. **Explanation:** We recognized that $10x^2$ is $(\sqrt{10}x)^2$ and $9$ is $3^2$, so the expression is a difference of squares and can be factored accordingly. **Final answer:** $$10x^2 - 9 = (\sqrt{10}x - 3)(\sqrt{10}x + 3)$$