Question

Which expressions are equivalent to 25x4 −64? Select three options.

25x4 + 40x − 40x − 64
25x4 + 13x − 13x − 64
(5x2 + 8)(5x2 − 8)
(x2 + 13)(x2 – 13)
(5x2 – 8)2

Answer 1

Answers: 1, 2, and 3.

Reason:
- 25x4 + 40x − 40x − 64 = 25x^4 − 64 (40x − 40x cancels).
- 25x4 + 13x − 13x − 64 = 25x^4 − 64 (13x − 13x cancels).
- (5x2 + 8)(5x2 − 8) = (5x^2)^2 − 8^2 = 25x^4 − 64 (difference of squares).

(4) expands to x^4 − 169, and (5) expands to 25x^4 − 80x^2 + 64, so they are not equivalent.