Math Problem Statement

Simplify each expression by combining similar terms. a²b²+3a²b²-a²b²

Solution

Let's simplify the given expression:

a2b2+3a2b2a2b2a^2b^2 + 3a^2b^2 - a^2b^2

We can combine like terms, where the terms with a2b2a^2b^2 can be added or subtracted:

(1a2b2+3a2b21a2b2)(1a^2b^2 + 3a^2b^2 - 1a^2b^2)

This simplifies to:

(1+31)a2b2=3a2b2(1 + 3 - 1) a^2b^2 = 3a^2b^2

So, the simplified expression is:

3a2b23a^2b^2

Would you like any further clarification on this?

Here are 5 related questions for you:

  1. How do you combine like terms with different powers?
  2. What are some real-life applications of expressions like a2b2a^2b^2?
  3. Can you simplify expressions with variables raised to different powers?
  4. How would you factor 3a2b23a^2b^2?
  5. What happens when you multiply terms with exponents, such as a2×b2a^2 \times b^2?

Tip: Always look for common factors or terms that have the same variable powers when combining like terms!

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Math Problem Analysis

Mathematical Concepts

Algebra
Like Terms
Polynomial Simplification

Formulas

Summation of like terms: (c₁x + c₂x + c₃x) = (c₁ + c₂ + c₃)x

Theorems

Properties of Addition in Algebra

Suitable Grade Level

Grades 6-8