Question

15. Which of the following expressions are equivalent?

1. (x-4)² - 1
11. x² - 8x - 17
II.
III. x² + 15
IV.X² - 8x + 15
V. (x - 5)(x-3)
VI.X2 - 17
A.
B.
C.
D.
IV and V
I and II
I, IV, V
I, III, V

Answer 1

I, IV, V

Explanation:

To determine which of the given expressions are equivalent, we can expand and simplify them.

I. (x - 4)² - 1

Expanding the square, we get:

(x - 4)² = x² - 8x + 16

So, (x - 4)² - 1 = x² - 8x + 15

II. x² - 8x - 17

III. x² + 15

IV. x² - 8x + 15

V. (x - 5)(x - 3)

Expanding the product, we get:

(x - 5)(x - 3) = x² - 8x + 15

VI. x² - 17

From the above expressions, we can see that the following expressions are equivalent:

I. (x - 4)² - 1 and IV. x² - 8x + 15

Also, V. (x - 5)(x - 3) is equivalent to both I. and IV.

Therefore, the answer is (C) I, IV, V.