Let's expand each of the given expressions using standard algebraic formulas:

1. $(12ab + 5c)(12ab - 5c)$

This is a difference of squares formula:
$(x + y)(x - y) = x^2 - y^2$

So:
$(12ab + 5c)(12ab - 5c) = (12ab)^2 - (5c)^2$ $= 144a^2b^2 - 25c^2$

2. $(3a - 6)^2$

This is a square of a binomial formula:
$(x - y)^2 = x^2 - 2xy + y^2$

So:
$(3a - 6)^2 = (3a)^2 - 2(3a)(6) + (6)^2$ $= 9a^2 - 36a + 36$

3. $(a + 4b + 8)^2$

This is a square of a trinomial formula:
$(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz$

So:
$(a + 4b + 8)^2 = a^2 + (4b)^2 + (8)^2 + 2(a)(4b) + 2(a)(8) + 2(4b)(8)$ $= a^2 + 16b^2 + 64 + 8ab + 16a + 64b$ Thus: $a^2 + 16b^2 + 64 + 8ab + 16a + 64b$

4. $(9p + 6q)(9p - 6q)$

This is also a difference of squares:
$(9p + 6q)(9p - 6q) = (9p)^2 - (6q)^2$ $= 81p^2 - 36q^2$

5. $(7x + 7y)^2$

This is a square of a binomial:
$(7x + 7y)^2 = (7x)^2 + 2(7x)(7y) + (7y)^2$ $= 49x^2 + 98xy + 49y^2$

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Do you want further clarification on any of the steps or detailed explanations?

Here are 5 related questions for further practice:

1. Expand $(5a + 3)(5a - 3)$.
2. Simplify $(2x + 4y)^2$.
3. Find the expansion of $(x - 7y - 9)^2$.
4. What is the expansion of $(4m + 5n)(4m - 5n)$?
5. Simplify $(6x + 8)^2$.

Tip: When expanding expressions, recognize common formulas like the square of a binomial or the difference of squares to speed up the process.