(x-2y).jpeg "(x^2+2xy+y^2)(x-2y)")
Expanding the Expression: (x² + 2xy + y²) (x - 2y)
This expression involves multiplying a trinomial (x² + 2xy + y²) by a binomial (x - 2y). We can expand this using the distributive property or FOIL method.
Distributive Property
The distributive property states that a(b + c) = ab + ac. Applying this to our expression:
(x² + 2xy + y²) (x - 2y) = (x² + 2xy + y²) * x + (x² + 2xy + y²) * (-2y)
Now we distribute again for each term:
= x²(x) + 2xy(x) + y²(x) + x²(-2y) + 2xy(-2y) + y²(-2y)
Simplifying the multiplication:
= x³ + 2x²y + xy² - 2x²y - 4xy² - 2y³
Combining Like Terms
Now we combine the terms with the same variables and exponents:
= x³ + (2x²y - 2x²y) + (xy² - 4xy²) - 2y³
= x³ - 3xy² - 2y³
Final Result
Therefore, the expanded form of (x² + 2xy + y²) (x - 2y) is x³ - 3xy² - 2y³.
Note: It's important to notice that the trinomial (x² + 2xy + y²) is a perfect square trinomial, which is the square of (x + y). This can be used to simplify the expansion even further.