Reduce the following rational expression to the lowest form

4x(x - 1)

Step-by-step explanation:

Factor the numerator and denominator

64 - 64x ← factor out 64x from both terms

= 64x( - 1) ← difference of squares

= 64x(x² - 1)(x² + 1) ← x² - 1 is also a difference of squares

= 64x(x - 1)(x + 1)(x² + 1)

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(8x² + 8)(2x + 2) ← factor out 8 and 2 from each factor

= 8(x² + 1) × 2(x + 1)

= 16(x² + 1)(x + 1)

Then expression can be written as

← cancel (x² + 1) and (x + 1) on numerator/ denominator

= ← cancel common factor 16 on numerator/ denominator

= 4x(x - 1)

probability for j is 1/4

while

a is 1/6