%5E2-expanded-form.jpeg "(3x-4)^2 Expanded Form")
Expanding (3x-4)^2
The expression (3x-4)^2 represents the square of the binomial (3x-4). To expand this, we can use the FOIL method or the square of a binomial pattern.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method involves multiplying each term in the first binomial by each term in the second binomial:
- First: (3x) * (3x) = 9x^2
- Outer: (3x) * (-4) = -12x
- Inner: (-4) * (3x) = -12x
- Last: (-4) * (-4) = 16
Adding all the terms together, we get:
9x^2 - 12x - 12x + 16
Finally, combining like terms, we obtain the expanded form:
(3x-4)^2 = 9x^2 - 24x + 16
Using the Square of a Binomial Pattern
The square of a binomial pattern states that (a-b)^2 = a^2 - 2ab + b^2. Applying this pattern to our expression:
- a = 3x
- b = 4
Substituting into the pattern, we get:
(3x)^2 - 2(3x)(4) + (4)^2
Simplifying, we get:
9x^2 - 24x + 16
Therefore, both methods lead to the same expanded form: (3x-4)^2 = 9x^2 - 24x + 16.