Question

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

Answer 1

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)]