(-2x^2y^4)^2+(6x^3y^3)(2xy^5)

Jasonbradley

2 min read

·

Jun 16, 2024

29

Share

Simplifying the Expression: (-2x^2y^4)^2 + (6x^3y^3)(2xy^5)

This article will guide you through the process of simplifying the expression (-2x^2y^4)^2 + (6x^3y^3)(2xy^5).

Understanding the Rules

Before we start simplifying, let's remember some basic rules:

• Exponents: When raising a product to a power, we raise each factor to that power: (ab)^n = a^n * b^n
• Multiplication of Variables: When multiplying variables with the same base, we add their exponents: x^m * x^n = x^(m+n)

Simplifying the Expression

Let's break down the expression step-by-step:

1. Simplify the first term:

   • (-2x^2y^4)^2 = (-2)^2 * (x^2)^2 * (y^4)^2 = 4x^4y^8

2. Simplify the second term:

   • (6x^3y^3)(2xy^5) = 6 * 2 * x^3 * x * y^3 * y^5 = 12x^4y^8

3. Combine the simplified terms:

   • 4x^4y^8 + 12x^4y^8 = 16x^4y^8

Conclusion

The simplified expression for (-2x^2y^4)^2 + (6x^3y^3)(2xy^5) is 16x^4y^8. This process highlights the importance of understanding exponent rules and variable multiplication for simplifying complex algebraic expressions.