x(2x%5E5y%5E2)%2B7x%5E9y%5E5.jpeg "(-8x^4y^3)x(2x^5y^2)+7x^9y^5")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through simplifying the algebraic expression (-8x^4y^3)x(2x^5y^2)+7x^9y^5.
Understanding the Expression
The given expression involves multiplication of terms with exponents. Let's break it down:
- Terms: The expression has two main terms:
(-8x^4y^3)x(2x^5y^2)7x^9y^5
- Exponents: Each term has variables with exponents. For instance,
x^4meansxmultiplied by itself four times. - Multiplication: The terms are connected by addition, indicating we need to simplify each term separately before combining them.
Simplifying the First Term
Let's simplify (-8x^4y^3)x(2x^5y^2):
- Combine the coefficients: Multiply the numerical coefficients:
-8 * 1 * 2 = -16 - Multiply the x terms: Apply the rule of exponents for multiplication:
x^4 * x * x^5 = x^(4+1+5) = x^10 - Multiply the y terms: Similarly,
y^3 * y^2 = y^(3+2) = y^5
Therefore, the simplified form of the first term is -16x^10y^5.
Simplifying the Second Term
The second term, 7x^9y^5, is already in its simplest form.
Combining the Simplified Terms
Now, we can combine the simplified terms:
-16x^10y^5 + 7x^9y^5
Since the terms have the same variables with the same exponents, we can simply combine the coefficients:
(-16 + 7)x^9y^5
Finally, we get the simplified form of the expression:
-9x^9y^5
Conclusion
By applying the rules of exponents and simplifying each term individually, we were able to simplify the given algebraic expression to -9x^9y^5. This process highlights the importance of understanding the fundamental concepts of algebra for simplifying complex expressions.