Answer to Question #128914 in Algebra for Gregg

Question

Simplify next expression t³-3t²s-s³+3ts² and calculate if t=14, s=3

Answer 1

It is given that we have to find expression value at

$t^3-3t^2s-s^3+3ts^2\\ when \,t=14 \, and \, s=3$

$t^3-s^3-3t^2s+3ts^2\\ =(t^3-s^3)-3ts(t-s)\\ =(t-s)(t^2+s^2+ts)-3ts(t-s)\\ =(t-s)(t^2+s^2-2ts)\\ (t-s)(t-s)^2\\ =(t-s)^3$

Now putting the value of t and s we get:

$(14-3)^3\\ =(11)^3\\ =1331$