Final answer:
The equivalent expression for the formula (2x - 3y)(3x + 4y) is found by applying the FOIL method and combining like terms, which results in 6x² - xy - 12y².
Step-by-step explanation:
The question asks which expression is an equivalent way of expressing the formula (2x - 3y)(3x + 4y). To find the equivalent expression, we must apply the FOIL method for multiplying two binomials. The FOIL method stands for First, Outer, Inner, Last, which represents the terms that need to be multiplied together.
- First: Multiply the first terms in each binomial: (2x) and (3x) which gives 6x².
- Outer: Multiply the outer terms in the binomials: (2x) and (4y) which gives 8xy.
- Inner: Multiply the inner terms in the binomials: (-3y) and (3x) which gives -9xy.
- Last: Multiply the last terms in each binomial: (-3y) and (4y) which gives -12y².
Finally, we combine like terms to get the resulting polynomial:
6x² + 8xy - 9xy - 12y²
Simplify by combining the xy terms:
6x² - xy - 12y²
Therefore, the equivalent expression for the formula (2x - 3y)(3x + 4y) is 6x² - xy - 12y².