1. (12ab + 5c)(12ab - 5c)
2.(3a - 6)²
3.(a+ 4b + 8)²
4.(9p + 6q)(9p - 6q)
5.(7x + 7y)²

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.

1. (12ab + 5c)(12ab - 5c)
2.(3a - 6)²
3.(a + 4b + 8)²
4.(9p + 6q)(9p - 6q)
5.(7x + 7y)²

Learn how to expand polynomials and binomials using algebraic formulas, including the difference of squares and the square of a binomial. This detailed step-by-step solution covers expressions like (12ab + 5c)(12ab - 5c) and (7x + 7y)². Suitable for students in Grades 9-10.

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