Factor completely: 3x^2(4x2 + 1)^8 + 64x^4(4x2 + 1)^7.

x^2(4x^2+1)^7(76x^2+3)

how did you solve this??? I am so los.

3x^2(4x2 + 1)^8 + 64x^4(4x2 + 1)^7

Notice that x^2 is a factor of each term, and so is a power of (4x^2+1)
So, factoring them out, we have

x^2 (4x^2+1)^7 (3(4x^2+1)+64x^2)
3(4x^2+1)+64x^2 = 12x^2+3+64x^2 = 76x^2+3

and that's Tony's answer

To factor the given expression completely, we can start by factoring out the common factor, which is (4x^2 + 1)^7.

Let's rewrite the expression:

3x^2(4x^2 + 1)^8 + 64x^4(4x^2 + 1)^7

Now we can factor out (4x^2 + 1)^7 as a common factor:

(4x^2 + 1)^7(3x^2(4x^2 + 1) + 64x^4)

Next, let's simplify the expression inside the parentheses:

3x^2(4x^2 + 1) + 64x^4

Multiplying 3x^2 by 4x^2, we get 12x^4, and multiplying 3x^2 by 1, we get 3x^2. Therefore, we have:

12x^4 + 3x^2 + 64x^4

Combining like terms, we get:

76x^4 + 3x^2

Finally, we can rewrite the factored expression as:

(4x^2 + 1)^7(76x^4 + 3x^2)

So, the expression 3x^2(4x^2 + 1)^8 + 64x^4(4x^2 + 1)^7 is factored completely as (4x^2 + 1)^7(76x^4 + 3x^2).