https://file.aiquickdraw.com/mathbot/file/1728974878972rsawqpgy.jpg

The expression extracted from the image is:

\[
3(2x - 1)^2(8x - 1)
\]

To simplify this expression, we will first expand \((2x - 1)^2\) and then multiply by \((8x - 1)\).

1. \((2x - 1)^2 = (2x - 1)(2x - 1)\)
   \[
   (2x - 1)(2x - 1) = 4x^2 - 4x + 1
   \]

2. Multiply by \((8x - 1)\):
   \[
   3 \times (4x^2 - 4x + 1)(8x - 1)
   \]

Now, expanding this:

\[
3 \times \left[ (4x^2)(8x) + (4x^2)(-1) + (-4x)(8x) + (-4x)(-1) + (1)(8x) + (1)(-1) \right]
\]

\[
3 \times \left[ 32x^3 - 4x^2 - 32x^2 + 4x + 8x - 1 \right]
\]

\[
3 \times (32x^3 - 36x^2 + 12x - 1)
\]

Finally, multiply the terms by 3:

\[
96x^3 - 108x^2 + 36x - 3
\]

Thus, the simplified expression is:

\[
96x^3 - 108x^2 + 36x - 3
\]

Would you like further details on any part of this process? Here are some related questions you might want to explore:

1. How do you expand binomials like \((2x - 1)^2\)?
2. How does the distributive property apply in expanding terms?
3. Can this expression be factored back?
4. What would happen if the powers in the expression were higher?
5. How can such expressions be used in real-world applications?

**Tip:** When expanding polynomials, always organize terms by degree (powers of \(x\)) to simplify calculations.

Simplify the expression 3(2x - 1)^2(8x - 1).

Simplify the polynomial expression 3(2x - 1)^2(8x - 1) with a detailed step-by-step solution. Learn how to expand binomials and apply the distributive property for higher-order terms. Suitable for students in Grades 9-12.

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