Math Problem Statement

Expand and simplify x(4x - 2) + x(5x + 6)

Solution

The given expression is:

x(4x2)+x(5x+6)x(4x - 2) + x(5x + 6)

Step 1: Expand each term

Distribute xx in both expressions:

x(4x2)=4x22xx(4x - 2) = 4x^2 - 2x x(5x+6)=5x2+6xx(5x + 6) = 5x^2 + 6x

Step 2: Combine the expanded terms

Now add the two results:

4x22x+5x2+6x4x^2 - 2x + 5x^2 + 6x

Step 3: Simplify by combining like terms

Combine x2x^2-terms and xx-terms:

(4x2+5x2)+(2x+6x)=9x2+4x(4x^2 + 5x^2) + (-2x + 6x) = 9x^2 + 4x

Final Answer:

9x2+4x9x^2 + 4x

Would you like a detailed explanation of any step? Here are some related questions to expand your understanding:

  1. How do you distribute variables in algebraic expressions?
  2. What are like terms, and why do we combine them?
  3. How do you handle expressions with more than two terms?
  4. What are some real-world examples where expanding and simplifying expressions is useful?
  5. How does factoring relate to this process?

Tip: Always double-check your work by re-expanding the simplified result to verify its correctness!

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Simplification

Formulas

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

Theorems

Commutative Property of Addition
Distributive Property

Suitable Grade Level

Grades 8-10