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(-8x^4y^3)•(2x^5y^2)+7x^9y^5

2 min read Jun 16, 2024
(-8x^4y^3)•(2x^5y^2)+7x^9y^5

Simplifying Algebraic Expressions: A Step-by-Step Guide

This article will guide you through the simplification of the algebraic expression: (-8x^4y^3)•(2x^5y^2)+7x^9y^5.

Understanding the Expression

The expression involves multiplication and addition of terms with variables and exponents. Let's break down each part:

  • (-8x^4y^3)•(2x^5y^2): This part represents the multiplication of two monomials.
  • 7x^9y^5: This is a single monomial.

Simplifying the Expression

  1. Multiplication of Monomials:

    To multiply monomials, we multiply the coefficients and add the exponents of the same variables.

    • Coefficients: -8 * 2 = -16
    • x: x^4 * x^5 = x^(4+5) = x^9
    • y: y^3 * y^2 = y^(3+2) = y^5

    Therefore, (-8x^4y^3)•(2x^5y^2) simplifies to -16x^9y^5.

  2. Adding Like Terms:

    Now we have: -16x^9y^5 + 7x^9y^5

    Both terms have the same variables with the same exponents, making them like terms. To add them, we simply add their coefficients.

    • -16 + 7 = -9

    Therefore, the simplified expression is -9x^9y^5.

Conclusion

By applying the rules of multiplication and addition of monomials, we successfully simplified the expression (-8x^4y^3)•(2x^5y^2)+7x^9y^5 to -9x^9y^5.

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