Formula of a3+b3+c3?
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The formula for (a+b+c)³ is a³ + b³ + c³ + 3a²b + 3ab² + 3ac² + 3bc² + 6abc.
- This is a generalization of the binomial theorem, which states that for any two numbers a and b, (a+b)^n = a^n + (n choose 1) * a^(n-1) * b + (n choose 2) * a^(n-2) * b^2 + ... + b^n.
- This formula can be expanded for more than two numbers, as in this case.The 3 terms a³,b³,c³ are coming from (a+b+c)(a²+b²+c²)
- The 6 terms 3a²b,3ab²,3ac²,3bc² are coming from (a+b+c)(ab+bc+ca) and the last term 6abc is coming from (a+b+c)(abc)
- This formula is also known as Newton's Formulae. It is useful for solving polynomial equations, and in many other areas of mathematics and physics.
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