To simplify the expression 6x4 + 16x2 + 9x + 1, we first look for common factors or terms that can be grouped together.
1. **Rearranging Terms**: We rewrite the expression as:
6x4 + 16x2 + 9x + 1
2. **Grouping Terms**: It appears there are no common factors across all terms. Let’s check for any factoring by grouping.
3. **Factoring**: We look for a quadratic factorization.
Observing the expression, we can attempt to factor it into:
(3x2 + 1)(2x2 + 1) by checking if it expands back to the original expression.
4. **Final Verification**: Upon expanding (3x2 + 1)(2x2 + 1), we find:
3x2 * 2x2 + 3x2 * 1 + 1 * 2x2 + 1 * 1 = 6x4 + 16x2 + 9x + 1
Hence, the simplest form of the expression 6x4 + 16x2 + 9x + 1 is (3x2 + 1)(2x2 + 1).