Factor the expression and simplify as much as possible. 24x (x2 1) 4 (x3 1) 5 42x2 (x2 1) 5 (x3 1) 4

Answer: 120[4 (x^6 + x^3 + x^4 + x) + 7 (x^7 + x^4 + x^5 + x^2) ]

Step-by-step explanation:

=24x (x^2 + 1) 4 (x^3 + 1) 5 + 42x^2 (x^2 + 1) 5 (x^3 + 1) 4

Remove the brackets first

=[ (24x^3 + 24x) (4x^3 + 4) ]5 + [ (42x^4 + 42x^2) (5x^3 + 5) 4]

=[ (96x^6 + 96x^3 + 96x^4 + 96x) 5] + [ (210x^7 + 210x^4 + 210x^5 + 210x^2) 4]

= (480x^6 + 480x^3 + 480x^4 + 480x) + (840x^7 + 840x^4 + 840x^5 + 840x^2)

Then the common:

=[480 (x^6 + x^3 + x^4 + x) + 840 (x^7 + x^4 + x^5 + x^2) ]

=120[4 (x^6 + x^3 + x^4 + x) + 7 (x^7 + x^4 + x^5 + x^2) ]