Question 87

If (x - y) = 7, then what is the value of $$(x-15)^{3}-(y-8)^{3}$$ ?

Solution

To find : $$(x-15)^{3}-(y-8)^{3}$$

Let $$(x-15)=a$$ and $$(y-8)=b$$

Thus, we need to find : $$a^3-b^3$$ -----------(i)

=> $$x=a+15$$ and $$y=b+8$$ ---------(ii)

It is given that, $$(x-y)=7$$

Substituting values from equation (ii),

=> $$(a+15)-(b+8)=7$$

=> $$a-b+7=7$$

=> $$a-b=0$$

Cubing both sides, we get :

=> $$a^3-b^3-3ab(a-b)=0$$

=> $$a^3-b^3-3ab(0)=0$$

=> $$a^3-b^3=0$$

=> Ans - (A)

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