Please give me the best way for solving the problem of class 9th ncert math of Polynomials chapter of math of class 9th of exercise 2.5 of question no 13 what is the tricky way for solving this question
If x+y+z = 0, show that x3+y3+z3 = 3xyz.
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We know that,
x3+y3+z3-3xyz = (x +y+z)(x2+y2+z2–xy–yz–xz)
Now, according to the question, let (x+y+z) = 0,
then, x3+y3+z3 -3xyz = (0)(x2+y2+z2–xy–yz–xz)
⇒ x3+y3+z3–3xyz = 0
⇒ x3+y3+z3 = 3xyz