Math Problem Statement

Simplify the algebraic expression: 2x + 4y^2 - 6y^2 - 9 + 1 - x + 3x

Solution

PIL import Image import pytesseract

Load the uploaded image to extract text

image_path = '/mnt/data/17346377354983fnnejdi.jpg' image = Image.open(image_path)

Use OCR to extract text

extracted_text = pytesseract.image_to_string(image, config='--psm 6') extracted_text.strip()The extracted expression appears to have been misinterpreted as:
2a+4y26?94+1a2+3e2a + 4y^2 - 6? - 94 + 1 - a^2 + 3e

This may not fully match the original content. Let me manually correct the terms based on your image. The expression seems closer to:
2x+4y26y29+1x+3x2x + 4y^2 - 6y^2 - 9 + 1 - x + 3x

I'll now simplify this expression.### Given Expression: 2x+4y26y29+1x+3x2x + 4y^2 - 6y^2 - 9 + 1 - x + 3x

Step 1: Combine Like Terms

  • Group the xx-terms: 2xx+3x=4x2x - x + 3x = 4x
  • Group the y2y^2-terms: 4y26y2=2y24y^2 - 6y^2 = -2y^2
  • Combine constants: 9+1=8-9 + 1 = -8

Final Simplified Expression:

4x2y284x - 2y^2 - 8

Would you like a more detailed breakdown of the steps? Here are some related questions for further exploration:

  1. What are the basic rules for combining like terms in an algebraic expression?
  2. How do you simplify expressions involving multiple variables?
  3. How can you verify the correctness of your simplified expression?
  4. What is the importance of arranging terms in a particular order (e.g., xx-terms first)?
  5. How would this expression change if a specific value for xx or yy is substituted?

Tip: Always verify your simplified expression by substituting sample values into both the original and simplified versions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Expressions

Formulas

Combining like terms

Theorems

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Suitable Grade Level

Grades 6-8