Final answer:
The multiplication of the binomials (b+4)(b-4) is a difference of squares problem, which simplifies to b² - 16 after the middle terms cancel each other out.
Step-by-step explanation:
The student's question involves the multiplication of two binomials which are special cases where the binomials are conjugates of each other, in this case, (b+4)(b-4). This specific type of multiplication is an application of the difference of squares formula, a² - b² = (a + b)(a - b).
To multiply (b+4)(b-4), we use the formula:
- First, multiply the first term of each binomial: b * b = b²
- Next, multiply the outer terms: b * -4 = -4b (this term will cancel out with the term from the inner multiplication)
- Then, multiply the inner terms: 4 * b = 4b (this term will also cancel out with the term from the outer multiplication)
- Finally, multiply the last term of each binomial: 4 * -4 = -16
Since the middle terms (+4b and -4b) cancel each other out, the result simplifies to b² - 16, which demonstrates the difference of squares.