Question 69

If $$y = 2x + 1$$, then what is the value of $$(8x^3 - y^3 + 6xy)$$?

Solution

$$y=2x+1$$

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

Cubing on both sides, we get

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

$$8x^3-y^3-6xy\left(-1\right)=-1$$ [From (1)]

$$8x^3-y^3+6xy=-1$$

Hence, the correct answer is Option B

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