%5E2.jpeg "(2z-5)^2")
Expanding and Simplifying (2z-5)^2
The expression (2z-5)^2 represents the square of the binomial (2z-5). 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. It's a method for multiplying two binomials:
- First: Multiply the first terms of each binomial: (2z) * (2z) = 4z^2
- Outer: Multiply the outer terms: (2z) * (-5) = -10z
- Inner: Multiply the inner terms: (-5) * (2z) = -10z
- Last: Multiply the last terms: (-5) * (-5) = 25
Now, combine the terms: 4z^2 - 10z - 10z + 25
Finally, simplify by combining like terms: 4z^2 - 20z + 25
Using the Square of a Binomial Formula
The square of a binomial formula states: (a - b)^2 = a^2 - 2ab + b^2
In our case, a = 2z and b = 5. Applying the formula:
(2z - 5)^2 = (2z)^2 - 2(2z)(5) + 5^2
Simplifying the expression: 4z^2 - 20z + 25
Conclusion
Both methods lead to the same simplified expression: 4z^2 - 20z + 25. This is the expanded and simplified form of (2z-5)^2.