Could someone show me step by step how this answer was derived?

Question

4x*3(x^2+1)^2*2x+4(x^2+1)^3
= 4(x^2+1)^2(7x^2+1)

Answer 1

This one has to do with combining like terms and factoring. Start by combining all of the terms that are multiplied together in the first part of your expression:

4x * 3(x^2 + 1)^2 * 2x + 4(x^2 + 1)^3 = 24x^2 * (x^2 + 1)^2 + 4(x^2 + 1)^3

From here, you can factor out a 4 and a (x^2 + 1)^2 term from both parts:

= [4(x^2 + 1)^2] * [6x^2 + (x^2 + 1)]

Finally, you can combine everything in the second part to come up with the answer that you originally gave us:

= [4(x^2 + 1)^2] * [7x^2+1]