(4a%5E2b%5E3)-(10a%5E3b)(6b%5E4).jpeg "(2ab^2)(4a^2b^3)-(10a^3b)(6b^4)")
Simplifying the Expression: (2ab^2)(4a^2b^3)-(10a^3b)(6b^4)
This article will guide you through simplifying the given algebraic expression: (2ab^2)(4a^2b^3)-(10a^3b)(6b^4). We will use the basic rules of exponents and algebraic operations to achieve a simplified form.
1. Applying the Distributive Property
First, we need to distribute the multiplication across the parentheses:
- (2ab^2)(4a^2b^3) = (2 * 4)(a * a^2)(b^2 * b^3) = 8a^3b^5
- (10a^3b)(6b^4) = (10 * 6)(a^3)(b * b^4) = 60a^3b^5
2. Combining Like Terms
Now, we have: 8a^3b^5 - 60a^3b^5. Since both terms have the same variables and exponents, they are considered like terms. We can combine them by subtracting their coefficients:
8a^3b^5 - 60a^3b^5 = -52a^3b^5
Final Simplified Expression
Therefore, the simplified form of the given expression (2ab^2)(4a^2b^3)-(10a^3b)(6b^4) is -52a^3b^5.