Find the product of (6y−2)2.6y-22.

A.

36y2−24y+436y2-24y+4

B.

36y2+24y−436y2+24y-4

C.

36y2+436y2+4

D.

12y2−16y+4


To find the product of \((6y - 2)(6y - 2)\), which is the square of the binomial \((6y - 2)\), we use the formula for squaring a binomial:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

Here, \(a = 6y\) and \(b = 2\). Let's apply the formula:

\[
(6y - 2)^2 = (6y)^2 - 2(6y)(2) + (2)^2
\]

Now, calculate each term:

1. \( (6y)^2 = 36y^2 \)
2. \( -2(6y)(2) = -24y \)
3. \( (2)^2 = 4 \)

So, the expanded form is:

\[
36y^2 - 24y + 4
\]

The correct answer is:

\(\boxed{A.\ 36y^2 - 24y + 4}\)

Would you like further details or have any questions?

### Related Questions:
1. How would the expression change if the binomial was \(6y + 2\)?
2. Can you expand \((6y - 2)^3\) using the binomial theorem?
3. How do you factor \(36y^2 - 24y + 4\) back into its original binomial form?
4. What is the vertex form of the quadratic expression \(36y^2 - 24y + 4\)?
5. How does the discriminant help in determining the nature of roots for this quadratic equation?

### Tip:
When squaring a binomial, remember that the middle term is always twice the product of the two terms inside the binomial.

Learn how to find the product of (6y - 2)^2 with a detailed step-by-step solution. This problem involves algebraic concepts like binomial expansion and squaring a binomial. Suitable for students in Grades 7-9.

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