Multiply.

left parenthesis 2 x minus 9 right parenthesis squared

To multiply \( (2x - 9)^2 \), follow the steps below:

1. Apply the formula for squaring a binomial:  
   \[
   (a - b)^2 = a^2 - 2ab + b^2
   \]
   Here, \( a = 2x \) and \( b = 9 \).

2. Expand:  
   \[
   (2x - 9)^2 = (2x)^2 - 2(2x)(9) + (9)^2
   \]

3. Simplify each term:
   - \( (2x)^2 = 4x^2 \)
   - \( -2(2x)(9) = -36x \)
   - \( 9^2 = 81 \)

4. Combine the terms:  
   \[
   4x^2 - 36x + 81
   \]

Thus, the product is:
\[
4x^2 - 36x + 81
\]

Would you like any further explanation or details?

Here are 5 related questions:
1. How do you expand other binomials like \( (3x + 5)^2 \)?
2. What is the result of \( (x - 4)^2 \)?
3. How can you apply the distributive property to expand binomials?
4. What does the square of a trinomial look like?
5. How do you simplify polynomial expressions?

**Tip:** When squaring a binomial, remember to include the middle term, which is twice the product of the two terms in the binomial.

Learn how to expand and simplify (2x - 9)^2 using the binomial expansion formula. This detailed step-by-step solution covers key algebraic concepts like binomial expansion and provides useful examples. Suitable for students in Grades 8-10.

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