%5E2.jpeg "(4x-6y^3)^2")
Expanding the Square of a Binomial
In mathematics, expanding a binomial squared means writing it out as a product of itself and then simplifying the result. In this case, we're dealing with the binomial (4x - 6y³)²
Understanding the Concept
When we square a binomial, we are essentially multiplying it by itself: (4x - 6y³)² = (4x - 6y³) * (4x - 6y³)
Expanding the Expression
To expand the expression, we can use the distributive property or the FOIL method:
1. FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term of the first binomial by each term of the second binomial.
- First: (4x) * (4x) = 16x²
- Outer: (4x) * (-6y³) = -24xy³
- Inner: (-6y³) * (4x) = -24xy³
- Last: (-6y³) * (-6y³) = 36y⁶
2. Distributive Property
We can also use the distributive property to multiply each term in the first binomial by the entire second binomial.
- 4x * (4x - 6y³) = 16x² - 24xy³
- -6y³ * (4x - 6y³) = -24xy³ + 36y⁶
Simplifying the Result
After expanding, we combine like terms:
16x² - 24xy³ - 24xy³ + 36y⁶ = 16x² - 48xy³ + 36y⁶
Final Answer
Therefore, the expanded form of (4x - 6y³)² is 16x² - 48xy³ + 36y⁶.