Answer:
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1. 12x + 16y^2
Factor out the greatest common factor:
4(3x + 4y^2)
2. 25x^2yz - 10xz
Factor out the common factor 5xz:
5xz(5xy - 2)
3. a^2 - 9
This is a difference of squares, which can be factored as:
(a + 3)(a - 3)
4. 121 - 49x^2
This is a difference of squares:
(11 + 7x)(11 - 7x)
5. x^2 + 16x + 64
This is a perfect square trinomial:
(x + 8)^2
6. 4a^2 + 12ab + 9
This is a perfect square trinomial:
(2a + 3)^2
7. x^2 + 5x + 6
This can be factored into:
(x + 2)(x + 3)
8. x^2 - x - 20
This can be factored into:
(x - 5)(x + 4)
9. a^3 + b^3
This is a sum of cubes:
(a + b)(a^2 - ab + b^2)
10. 27x^3 - 8y^3
This is a difference of cubes:
(3x - 2y)(9x^2 + 6xy + 4y^2)
These are the completely factored forms of the given expressions.