%5E2.jpeg "(-6x^2+7y^3)^2")
Expanding the Square of a Binomial: (-6x² + 7y³)²
This article will guide you through the process of expanding the square of a binomial expression: (-6x² + 7y³)²
Understanding the Concept
Squaring a binomial means multiplying it by itself. In this case:
(-6x² + 7y³)² = (-6x² + 7y³) * (-6x² + 7y³)
Applying the FOIL Method
The FOIL method is a helpful mnemonic for expanding binomials:
- First: Multiply the first terms of each binomial: (-6x²) * (-6x²) = 36x⁴
- Outer: Multiply the outer terms: (-6x²) * (7y³) = -42x²y³
- Inner: Multiply the inner terms: (7y³) * (-6x²) = -42x²y³
- Last: Multiply the last terms: (7y³) * (7y³) = 49y⁶
Combining Like Terms
Now, add the results together and combine any like terms:
36x⁴ - 42x²y³ - 42x²y³ + 49y⁶
Simplifying, we get:
36x⁴ - 84x²y³ + 49y⁶
Final Result
Therefore, the expanded form of (-6x² + 7y³)² is 36x⁴ - 84x²y³ + 49y⁶.
Key Takeaways
- Squaring a binomial involves multiplying it by itself.
- The FOIL method is a useful tool for expanding binomials.
- Combining like terms is essential for simplifying the final expression.