Question

If xy = 1, which is equivalent to x(x – 1)(y + 1)?

A) x – 1
B) x2 – 1
C) x2 – x
D) x2 – x + y – 1

Answer 1

B) x^2 – 1

Explanation:

x(x – 1)(y + 1)

FOIL (x-1)(y+1)

firsy: xy

outer 1x

inner -1y

last (1)(-1) =-1

Add them together xy +x-y-1

x( xy +x-y-1)

Replace xy with 1

x( 1+x-y-1)

x(+x-y)

Distribute

x^2-xy

But xy=1

x^2 -1