%5E2.jpeg "(-1+2d)^2")
Expanding (-1 + 2d)^2
The expression (-1 + 2d)^2 represents the square of a binomial. To expand 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 helps us multiply two binomials by systematically multiplying each term in the first binomial with each term in the second binomial.
In this case, we have:
(-1 + 2d) * (-1 + 2d)
Applying the FOIL method:
- First: (-1) * (-1) = 1
- Outer: (-1) * (2d) = -2d
- Inner: (2d) * (-1) = -2d
- Last: (2d) * (2d) = 4d^2
Combining all the terms:
1 - 2d - 2d + 4d^2 = 4d^2 - 4d + 1
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 = -1 and b = 2d. Substituting these values into the formula:
(-1 + 2d)^2 = (-1)^2 + 2(-1)(2d) + (2d)^2
Simplifying:
= 1 - 4d + 4d^2 = 4d^2 - 4d + 1
Therefore, both methods lead to the same result: (-1 + 2d)^2 = 4d^2 - 4d + 1.