How do you factor this problem?
Hello,
The problem is:
3x^2(4x^2+1)^8 + 64x^4(4x^2+1)^7
The question says to factor completely, but I have no idea how to approach this problem.
The answer says x^2(4x^2+1)^7(76x^2+3) but I do not know how the answer was reached.
Thank you.
Update:Thank you everyone. I will choose the best answer shortly.
In the meantime, could someone help me solve this problem?
http://answers.yahoo.com/question/index;_ylt=AieTo...
Thank you.
Comments
So we can factor out an x^2 and a (4x^2+1)^7
x^2(4x^2+1)^7 (3(4x^2+1) + 64x^2))
x^2(4x^2+1)^7 (12x^2+3 + 64x^2)
Then combine like terms on the right side:
(x^2)(4x^2+1)^7 (76x^2 + 3)
You will see that on both sides of the plus sign that there are common factors of x^2 and (4x^2+1)^7
So, you simply factor those out: x^2(4x^2+1)^7[3(4x^2)+64x^2]
Then simply multiply out the inside expression which equals 76x^2+3
The common factor to both terms is x^2(4x^2+1)^7
That leaves 3(4x^2+1) + 64x^2
Then the whole thing is x^2(4x^2+1)^7[3(4x^2+1) + 64x^2]
I hope this helps
Remember, factors can be x^4, but they can also be more complicated expressions like in this problem.
Dizzle got me on that last term. He is correct. x^2(4x^2+1)^7[72x^2 + 3]
x^2(4x^2+1)^7[3(4x^2+1) + 64x^2]
= x^2(4x^2+1)^7 [12x^2 +3 +64x^2]
= x^2(4x^2 +1)^7(76x^2 +3)
Its not an answer, its just reduced to find the answer.