https://file.aiquickdraw.com/mathbot/file/1727345044939ndhfa39n.jpg

Let's go through each option step-by-step to check for correctness:

**(a) \((2x + 3)(2x + 3) = 2x^2 + 12x + 9\)**  
This expression is the square of a binomial, \((2x + 3)^2\):
\[
(2x + 3)(2x + 3) = (2x)^2 + 2(2x)(3) + 3^2 = 4x^2 + 12x + 9
\]
The right-hand side should be \(4x^2 + 12x + 9\), not \(2x^2 + 12x + 9\).  
**This is incorrect.**

**(b) \((4y - 3z)(4y - 3z) = 16y^2 - 24yz + 9z^2\)**  
This is the square of a binomial \((4y - 3z)^2\):
\[
(4y - 3z)(4y - 3z) = (4y)^2 - 2(4y)(3z) + (3z)^2 = 16y^2 - 24yz + 9z^2
\]
This is correct.

**(c) \((2a + b)(2a - b) = 4a^2 - b^2\)**  
This is a difference of squares:
\[
(2a + b)(2a - b) = (2a)^2 - b^2 = 4a^2 - b^2
\]
This is correct.

**(d) \((2x + y)(x - y) = 2x^2 + xy - y^2\)**  
Expanding the left-hand side:
\[
(2x + y)(x - y) = 2x(x - y) + y(x - y) = 2x^2 - 2xy + xy - y^2 = 2x^2 - xy - y^2
\]
The correct expansion should be \(2x^2 - xy - y^2\), not \(2x^2 + xy - y^2\).  
**This is incorrect.**

**(e) \(2a(3a^2 - 2b + 3) = 6a^3 - 4ab + 6b\)**  
Distribute the \(2a\):
\[
2a(3a^2 - 2b + 3) = 2a(3a^2) + 2a(-2b) + 2a(3) = 6a^3 - 4ab + 6a
\]
The last term should be \(6a\), not \(6b\).  
**This is incorrect.**

### Summary:
The incorrect options are:
- **(a)**
- **(d)**
- **(e)**

Since the question asks for **which one** is incorrect, and it only allows for a single choice, we can infer that **(a)** is the most obvious incorrect answer from the list.

Which of the following products is incorrect? (a) (2x + 3)(2x + 3) = 2x^2 + 12x + 9 (b) (4y - 3z)(4y - 3z) = 16y^2 - 24yz + 9z^2 (c) (2a + b)(2a - b) = 4a^2 - b^2 (d) (2x + y)(x - y) = 2x^2 + xy - y^2 (e) 2a(3a^2 - 2b + 3) = 6a^3 - 4ab + 6b

This problem tests knowledge of algebraic expansions, including binomial expansions and difference of squares. It asks students to identify the incorrect product from a set of expanded expressions. This example includes both correct and incorrect applications of the binomial square and difference of squares formulas. Suitable for students in Grades 9-10.

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