Completing the Operation: (-a - 6b + 4)^3ab
In this article, we will delve into the process of completing the operation for the given algebraic expression: (-a - 6b + 4)^3ab.
Understanding the Expression
The expression consists of several components:
- (-a - 6b + 4): This is the inner expression, which is raised to a power.
- ^3: This is the exponent, indicating that the inner expression is raised to the power of 3.
- ab: This is the outer expression, which is multiplied by the result of the inner expression raised to the power of 3.
Step-by-Step Approach
To complete the operation, we will follow these steps:
Simplify the Inner Expression: First, we need to simplify the inner expression (-a - 6b + 4). We can do this by combining the like terms: (-a - 6b + 4) = -a - 6b + 4
Raise the Inner Expression to the Power of 3: Next, we need to raise the simplified inner expression to the power of 3: (-a - 6b + 4)^3 = (-a - 6b + 4) × (-a - 6b + 4) × (-a - 6b + 4)
Simplify the Exponent Expansion: Expanding the exponent, we get: (-a - 6b + 4)^3 = -a^3 - 18a^2b + 108ab^2 - 216b^3 - 12a^2 + 72ab - 144b^2 + 4a + 24b - 64
Multiply by the Outer Expression: Finally, we need to multiply the result of the inner expression raised to the power of 3 by the outer expression ab: (-a^3 - 18a^2b + 108ab^2 - 216b^3 - 12a^2 + 72ab - 144b^2 + 4a + 24b - 64) × ab
The final result is the completed operation of the given expression: (-a - 6b + 4)^3ab.
Remember, the order of operations is crucial when working with algebraic expressions. By following the steps outlined above, you can successfully complete the operation and simplify the expression.