%5E2.jpeg "(6m-2)^2")
Expanding (6m-2)^2
The expression (6m-2)^2 represents the square of the binomial (6m-2). To expand this, we can use the FOIL method or the square of a difference formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials:
- First: Multiply the first terms of each binomial: (6m) * (6m) = 36m^2
- Outer: Multiply the outer terms of the binomials: (6m) * (-2) = -12m
- Inner: Multiply the inner terms of the binomials: (-2) * (6m) = -12m
- Last: Multiply the last terms of each binomial: (-2) * (-2) = 4
Now, combine all the terms: 36m^2 - 12m - 12m + 4
Finally, simplify by combining like terms: 36m^2 - 24m + 4
Using the Square of a Difference Formula
The square of a difference formula states: (a - b)^2 = a^2 - 2ab + b^2
In our case, a = 6m and b = 2. Applying the formula:
(6m - 2)^2 = (6m)^2 - 2(6m)(2) + (2)^2
Expanding and simplifying: 36m^2 - 24m + 4
Therefore, both methods lead to the same expanded form: (6m-2)^2 = 36m^2 - 24m + 4