Question 71

If $$2x + 3y + 1 = 0$$, then what is the value of $$\left(8x^3 + 8 + 27y^3 - 18xy \right)$$?

Solution

$$2x+3y+1=0$$

$$2x+3y=-1$$........(1)

Cubing on both sides,

$$8x^3+27y^3+3.2x.3y\left(2x+3y\right)=-1$$

$$8x^3+27y^3+18xy\left(-1\right)=-1$$

$$8x^3+27y^3-18xy+8=-1+8$$

$$8x^3+27y^3-18xy+8=7$$

Hence, the correct answer is Option B

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