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The factors for Choose one of the factors of 27x3 + 512y3 are ... (3x + 8y) and (9x^2 - 24xy + 64x^2) ?
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27x^3 +512y^3 = 0 27x^3=-512y^3 -y/x =(27/512)^(1/3) y/x =(-3/8) 3x+8y=0 Therefore, it is a factor of 27x^3 +512y^3 use long division, (27x^3 +512y^3)/(3x+8y) the quotient is not (9x^2 - 24xy + 64x^2) but (9x^2 - 24xy + 64y^2)
27x3 + 512y3 = (3x)^3 + (8y)^3 = (3x+8y) [ (3x)^2 - (3x)(8y) + (8y)^2 ] = (3x+8y) (9x^2 -24xy + 64y^2) Identity used: \(a^3+b^3 = (a+b)(a^2-ab+b^2)\)
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