%5E2-expand.jpeg "(2x-3)^2 Expand")
Expanding (2x-3)^2
The expression (2x-3)^2 represents the square of the binomial (2x-3). To expand this expression, we can use the following methods:
1. Using the FOIL method
FOIL stands for First, Outer, Inner, Last. This method helps us to multiply each term of the first binomial with each term of the second binomial.
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x^2
- Outer: Multiply the outer terms: (2x) * (-3) = -6x
- Inner: Multiply the inner terms: (-3) * (2x) = -6x
- Last: Multiply the last terms: (-3) * (-3) = 9
Now, combine all the terms: 4x^2 - 6x - 6x + 9
Finally, simplify by combining like terms: 4x^2 - 12x + 9
2. Using the square of a binomial formula
The formula for the square of a binomial is: (a - b)^2 = a^2 - 2ab + b^2
In our case, a = 2x and b = 3.
Substitute these values into the formula:
(2x - 3)^2 = (2x)^2 - 2(2x)(3) + (3)^2
Simplify: 4x^2 - 12x + 9
Conclusion
Both methods lead to the same expanded form of (2x-3)^2, which is 4x^2 - 12x + 9. You can choose whichever method you find easier to use.