Answer:
Product = 4e^2 - d^2 - 3ed
Explanation:
- (-d + e) and (4e + d) are both binomials.
Since we're trying to find the product of two binomials, we can use the FOIL method, where:
- F refers to the product of the first two terms (-d and 4e),
- O refers to the product of the outer two terms (-d and d),
- I refers to the product of the inner two terms (e and 4e),
- and L refers to the product of the last two terms (e and d).
Thus, we find all the products and simplify:
(-d * 4e) + (-d * d) + (e * 4e) + (e * d)
-4ed - d^2 + 4e^2 + ed
4e^2 - d^2 + (-4ed + ed)
4e^2 - d^2 - 3ed
Thus, the product of (-d + e)(4e + d) is 4e^2 - d^2 - 3ed.