%5E2-answer.jpeg "(3x-4y)^2 Answer")
Expanding (3x - 4y)^2
The expression (3x - 4y)^2 represents the square of the binomial (3x - 4y). To expand this expression, 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 to multiply each term of the first binomial by each term of the second binomial.
- First: Multiply the first terms of each binomial: (3x) * (3x) = 9x²
- Outer: Multiply the outer terms of the binomials: (3x) * (-4y) = -12xy
- Inner: Multiply the inner terms of the binomials: (-4y) * (3x) = -12xy
- Last: Multiply the last terms of each binomial: (-4y) * (-4y) = 16y²
Finally, combine the like terms: 9x² - 12xy - 12xy + 16y² = 9x² - 24xy + 16y²
Using the Square of a Difference Formula
The square of a difference formula states: (a - b)² = a² - 2ab + b²
Applying this formula to our expression:
- a = 3x
- b = 4y
Substituting these values into the formula:
(3x - 4y)² = (3x)² - 2(3x)(4y) + (4y)²
Simplifying:
(3x - 4y)² = 9x² - 24xy + 16y²
Therefore, the expanded form of (3x - 4y)² is 9x² - 24xy + 16y². Both the FOIL method and the square of a difference formula lead to the same answer. Choose the method you find easiest to apply.