Question

4. Evaluate the expression (x + 5). (x – 5)2 for x = 3
a. 32
b. -16
c. 16
d. -32

Answer 1

The expression (x + 5)(x - 5) represents a difference of squares, which simplifies to 9a² - 25 when substituting x with 3a. Without further information on the value of 'a', we cannot provide a numerical answer.

Step-by-step explanation:

The student has asked to evaluate the expression (x + 5) · (x – 5) for x = 3a. Assuming there's a typo and the expression should read (x + 5) · (x – 5) without the extra '2' or it's indicating squaring the second term only, which changes the calculation. For our purposes, let's evaluate the original expression as a difference of squares without any exponent on the second term: (x + 5)(x - 5).

Substituting x = 3a into the expression yields:

1. (3a + 5) · (3a - 5)
2. Using the difference of squares, which is a² - b² = (a + b)(a - b), the expression simplifies to:
3. 9a² - 25

Without specific values for 'a', we cannot provide a numerical answer from the options given (32, -16, 16, -32). The student may have intended to include a term for 'a' or a specific numerical substitution, which could lead to one of these values. However, with the information provided, we can only simplify the expression algebraically.