Math Problem Statement

(7x^2 + x) - (9x^2 + 4x)

Solution

To simplify the expression (7x2+x)(9x2+4x)(7x^2 + x) - (9x^2 + 4x), follow these steps:

Step 1: Distribute the negative sign

Distribute the negative sign across the terms inside the second parentheses: (7x2+x)9x24x(7x^2 + x) - 9x^2 - 4x

This becomes: 7x2+x9x24x7x^2 + x - 9x^2 - 4x

Step 2: Combine like terms

  • Combine 7x27x^2 and 9x2-9x^2: 7x29x2=2x27x^2 - 9x^2 = -2x^2

  • Combine xx and 4x-4x: x4x=3xx - 4x = -3x

Step 3: Write the simplified result

2x23x-2x^2 - 3x

Final Answer:

2x23x-2x^2 - 3x


Would you like a more detailed explanation or help with related problems?

5 Related Questions:

  1. How do you simplify polynomial expressions with multiple variables?
  2. What is the significance of combining like terms in algebra?
  3. How can you factorize expressions like 2x23x-2x^2 - 3x?
  4. How does distributing a negative sign affect an expression?
  5. What are the rules for adding and subtracting polynomials?

Tip:

Always double-check your work by re-expanding or re-evaluating the steps to confirm accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Polynomial Expressions
Combining Like Terms

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Commutative Property of Addition
Associative Property of Addition

Suitable Grade Level

Grades 7-9