%5E2.jpeg "(5x-9)^2")
Expanding and Simplifying (5x - 9)^2
The expression (5x - 9)^2 represents the square of the binomial (5x - 9). To simplify this expression, we can use the FOIL method or the square of a binomial formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method involves multiplying each term of the first binomial by each term of the second binomial:
- First: (5x) * (5x) = 25x^2
- Outer: (5x) * (-9) = -45x
- Inner: (-9) * (5x) = -45x
- Last: (-9) * (-9) = 81
Adding all the terms together, we get:
(5x - 9)^2 = 25x^2 - 45x - 45x + 81
Finally, combining like terms, we have:
(5x - 9)^2 = 25x^2 - 90x + 81
Using the Square of a Binomial Formula
The square of a binomial formula states: (a - b)^2 = a^2 - 2ab + b^2
Applying this formula to our expression:
(5x - 9)^2 = (5x)^2 - 2(5x)(9) + (-9)^2
Simplifying:
(5x - 9)^2 = 25x^2 - 90x + 81
Conclusion
Both the FOIL method and the square of a binomial formula lead to the same simplified expression: 25x^2 - 90x + 81. This represents the expanded form of (5x - 9)^2.