Question 86

If m = - 4, n = - 2, then the value of $$m^3 - 3m^2 + 3m + 3n + 3n^2 + n^3$$ is

Solution

We are given that m = -4 and n = -2

Expression : $$m^3 - 3m^2 + 3m + 3n + 3n^2 + n^3$$

= $$(m^3 - 3m^2 + 3m - 1) + (n^3 + 3n^2 + 3n + 1)$$

= $$(m-1)^3 + (n+1)^3$$

= $$(-4-1)^3 + (-2+1)^3$$

= $$(-5)^3 + (-1)^3$$

= $$-125 - 1 = -126$$

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