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the binomial 8y^12+z^6 can be factored into a binomial and a trinomial. the binomial factor is (2y^4+z^2). whats the trinomial?

  • algebra -

    Just do the long division to get
    (2y^4 + z^2)(4y^8 - 2y^4z^2 + z^4)

  • algebra -

    or, you could recognize it as the sum of two cubes:

    = (2y^4)^3 + (z^2)^3
    = (2y^4 + z^2)((2y^4)^2 - (2y^4)(z^2) + (z^2)^2)
    = (2y^4 + z^2)(4y^8 - 2y^4z^2 + z^4)

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