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.

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