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(-8xy^3)(5x^3y^2)+3x^4y^5

2 min read Jun 16, 2024
(-8xy^3)(5x^3y^2)+3x^4y^5

Simplifying the Expression (-8xy^3)(5x^3y^2) + 3x^4y^5

This article will guide you through the process of simplifying the given algebraic expression: (-8xy^3)(5x^3y^2) + 3x^4y^5.

Understanding the Basics

Before we begin simplifying, let's recall some fundamental rules of algebra:

  • Multiplication of Variables: When multiplying variables with exponents, we add the exponents of the same base. For example, x^m * x^n = x^(m+n).
  • Multiplication of Coefficients: We multiply the numerical coefficients directly. For example, 2 * 3 = 6.

Simplifying the Expression

Let's break down the simplification process step by step:

  1. Multiply the first two terms:

    (-8xy^3)(5x^3y^2) = -40x^(1+3)y^(3+2) = -40x^4y^5

  2. Combine with the third term:

    -40x^4y^5 + 3x^4y^5 = (-40 + 3)x^4y^5

  3. Simplify:

    (-40 + 3)x^4y^5 = -37x^4y^5

Final Result

Therefore, the simplified form of the expression (-8xy^3)(5x^3y^2) + 3x^4y^5 is -37x^4y^5.

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