The product of two numbers is 16x^4 -1. If one number is 2x - 1, find the other.

The product = (16x 4 \-1) One number = (2x \- 1) Let the other number be A. (2x \- 1) A = (16x 4 \-1) ⇒ A = ⇒ A = ⇒ A = ⇒ A = ⇒ A = (2x \+ 1)(4x 2 \+ 1) ⇒ A = 2x(4x 2 \+ 1) \+ 1(4x 2 \+ 1) ⇒ A = 8x (2+1) \+ 2x \+ 4x 2 \+ 1 ⇒ A = 8x 3 \+ 4x 2 \+ 2x \+ 1 Hence, the other number is 8x 3 \+ 4x 2 \+ 2x \+ 1.