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Problem 17 - Entrance Test

If 2x + 3y = 12 and xy = 6, then 8x³ + 27y³ equals

Correct: A

8x\u00b3+27y\u00b3=(2x)\u00b3+(3y)\u00b3=(2x+3y)(4x\u00b2-6xy+9y\u00b2)=12[(2x+3y)\u00b2-18xy]=12[144-108]=12\u00b736=432.