Answer:
4x(x - 1)
Step-by-step explanation:
Factor the numerator and denominator
64[tex]x^{5}[/tex] - 64x ← factor out 64x from both terms
= 64x([tex]x^{4}[/tex] - 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
[tex]\frac{64x(x-1)(x+1)(x^2+1)}{16(x^2+1)(x+1)}[/tex] ← cancel (x² + 1) and (x + 1) on numerator/ denominator
= [tex]\frac{64x(x-1)}{16}[/tex] ← cancel common factor 16 on numerator/ denominator
= 4x(x - 1)
