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Answer:
Sure, let’s simplify these expressions:
1. **16x² + 8x + 81**
This is a quadratic expression. To simplify it, we can try factoring it or completing the square. However, it does not easily factor into simple binomials. So, it can be left as it is or expressed in terms of its roots if solved by the quadratic formula.
2. **9m² + 30m + 25**
This is a perfect square trinomial. It factors into:
\[
(3m + 5)²
\]
3. **x² + 2x + 1**
This is also a perfect square trinomial. It factors into:
\[
(x + 1)²
\]
Now for the second set:
1. **9a² - 6a + 1**
This is a perfect square trinomial. It factors into:
\[
(3a - 1)²
\]
2. **m² - 8m + 25**
This does not factor neatly into integers. To express it in vertex form, we complete the square:
\[
m² - 8m + 25 = (m - 4)² + 9
\]
3. **49b² - 28b + 4**
This does not factor neatly into simple binomials either. Completing the square:
\[
49b² - 28b + 4 = (7b - 2)²
\]