(x%5E2-xy%2B3y).jpeg "(x+2y)(x^2-xy+3y)")
Expanding (x + 2y)(x² - xy + 3y)
This expression involves multiplying two binomials, one with two terms and the other with three. To expand this, we can use the distributive property, also known as FOIL (First, Outer, Inner, Last) for binomials. Since we have a trinomial here, we can think of it as a slightly extended version of FOIL.
Here's how we break it down:
-
Distribute the first term of the first binomial:
- x * (x² - xy + 3y) = x³ - x²y + 3xy
-
Distribute the second term of the first binomial:
- 2y * (x² - xy + 3y) = 2x²y - 2xy² + 6y²
-
Combine the results:
- x³ - x²y + 3xy + 2x²y - 2xy² + 6y²
-
Simplify by combining like terms:
- x³ + x²y + 3xy - 2xy² + 6y²
Therefore, the expanded form of (x + 2y)(x² - xy + 3y) is x³ + x²y + 3xy - 2xy² + 6y².
Key Takeaway: The distributive property is a powerful tool for expanding algebraic expressions. It allows us to break down complex expressions into simpler terms, making them easier to understand and manipulate.