Logarithms (G12)
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Sum of cubes formula: \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\). Here \(27x^3 = (3x)^3\) and \(8y^3 = (2y)^3\), so \(a = 3x\), \(b = 2y\). Therefore: \((3x + 2y)((3x)^2 - (3x)(2y) + (2y)^2) = (3x + 2y)(9x^2 - 6xy + 4y^2)\).
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