https://file.aiquickdraw.com/mathbot/file/17263887063747zvs1g15.jpg

I can help you interpret the math work from the image. Here's what I see in the image:

1. **First part**:
   \[
   x^2 + 27x + 72
   \]
   This is a quadratic equation.

2. **Factoring the quadratic**:
   \[
   x^2 + 8x + 9x + 72
   \]
   The next step shows splitting the middle term:
   \[
   x(x + 8) + 9(x + 8)
   \]
   Factoring out common terms gives:
   \[
   (x + 8)(x + 9)
   \]
   So, the factorization of \(x^2 + 27x + 72\) is \((x + 8)(x + 9)\).

3. **Second part**:
   \[
   (4m^2 + 19mn + 12n^2)^2
   \]
   This is a binomial expansion problem. The expression inside the square could potentially be factored or expanded further.

Would you like more detailed steps for the second part? Or would you like to explore more questions based on this?

Here are 5 relative questions to expand this topic:
1. How do you determine the factors of a quadratic expression?
2. Can every quadratic be factored into two binomials?
3. What is the binomial theorem, and how can it help expand powers of polynomials?
4. How do you factor trinomial expressions like \(4m^2 + 19mn + 12n^2\)?
5. What are the steps for simplifying expressions raised to a power?

**Tip**: Always look for the greatest common factor before factoring quadratics or trinomials; it can simplify the process!

Factoring the quadratic equation x^2 + 27x + 72 and simplifying the expression (4m^2 + 19mn + 12n^2)^2.

Learn how to factor the quadratic equation x^2 + 27x + 72 into two binomials and explore the binomial expansion of (4m^2 + 19mn + 12n^2)^2. This detailed solution covers key algebraic concepts suitable for students in Grades 8-10.

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