(2y-7).jpeg "(2y-7)(2y-7)")
Expanding (2y - 7)(2y - 7)
This expression represents the product of two identical binomials, meaning it's a perfect square trinomial. We can expand this using the FOIL method or by applying the square of a difference formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial with each term in the second binomial:
- First: (2y) * (2y) = 4y²
- Outer: (2y) * (-7) = -14y
- Inner: (-7) * (2y) = -14y
- Last: (-7) * (-7) = 49
Now, combine the like terms:
4y² - 14y - 14y + 49 = 4y² - 28y + 49
Using the Square of a Difference Formula
The formula for the square of a difference is: (a - b)² = a² - 2ab + b²
In our case, a = 2y and b = 7. Substituting these values into the formula:
(2y - 7)² = (2y)² - 2(2y)(7) + 7²
Expanding this gives us:
(2y - 7)² = 4y² - 28y + 49
Conclusion
Both methods lead to the same result: (2y - 7)(2y - 7) = 4y² - 28y + 49.
This expanded form is a perfect square trinomial because it can be factored back into the original binomial form. The process of expanding and factoring such expressions is important in algebra and other fields of mathematics.