https://file.aiquickdraw.com/mathbot/file/1726154222859vdqnn2fq.jpg

The problem shown in the image asks to simplify the expression:

\[
7(6x^2 - 2x + 5) - 5(x^2 - 8) - 9x^2.
\]

Let's go through the steps to simplify this expression completely:

1. **Expand each term:**
   - For \( 7(6x^2 - 2x + 5) \):
     \[
     7 \times 6x^2 = 42x^2, \quad 7 \times (-2x) = -14x, \quad 7 \times 5 = 35.
     \]
     So, \( 7(6x^2 - 2x + 5) = 42x^2 - 14x + 35. \)

   - For \( -5(x^2 - 8) \):
     \[
     -5 \times x^2 = -5x^2, \quad -5 \times (-8) = 40.
     \]
     So, \( -5(x^2 - 8) = -5x^2 + 40. \)

2. **Combine all the terms:**
   \[
   42x^2 - 14x + 35 - 5x^2 + 40 - 9x^2.
   \]

3. **Combine like terms:**
   - Combine the \( x^2 \) terms: \( 42x^2 - 5x^2 - 9x^2 = 28x^2. \)
   - The \( x \) term remains as \( -14x. \)
   - Combine the constant terms: \( 35 + 40 = 75. \)

4. **Final simplified expression:**
   \[
   28x^2 - 14x + 75.
   \]

Let me know if you need more details or if you have any questions!

Here are some related questions you might explore:
1. How do you simplify expressions with multiple variables?
2. What are the steps for factoring polynomials?
3. How can you identify and combine like terms in an expression?
4. What is the distributive property and how is it used in algebra?
5. How do you simplify complex fractions?

**Tip:** When simplifying expressions, always carefully combine like terms and double-check each step to ensure accuracy.

Simplify the expression: 7(6x^2 - 2x + 5) - 5(x^2 - 8) - 9x^2

Learn how to simplify the polynomial expression 7(6x^2 - 2x + 5) - 5(x^2 - 8) - 9x^2 with a detailed step-by-step solution. This guide covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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