Question

Find the product of (–d + e)(4e + d)

Answer 1

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.