Final answer:
To multiply the conjugate binomials (8-c)(8+c), you apply the distributive property, which results in 64 - c^2, also known as the difference of squares.
Step-by-step explanation:
The question involves multiplying conjugate binomials, which is a concept in algebra within mathematics. The conjugate binomials in question are (8-c) and (8+c). When we multiply conjugates, we apply the distributive property (also known as the FOIL method for binomials), which results in the difference of squares.
To multiply the conjugate binomials (8-c) and (8+c), we perform the following steps:
- Multiply the first terms of each binomial (8 * 8).
- Multiply the outside terms (8 * c).
- Multiply the inside terms (-c * 8).
- Multiply the last terms of each binomial (-c * c).
Following these steps leads to this calculation:
(8 * 8) + (8 * c) - (c * 8) - (c * c) = 64 - c^2
Notice that the middle terms (8 * c and -c * 8) cancel each other out, leaving us with the difference of squares, which is the result of the product.