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How do you prove a3 b3 c3 3abc?

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How do you prove a3 b3 c3 3abc?

  1. = (a³+b³)+c³-3abc.
  2. = (a+b)³-3ab(a+b)+c³-3abc.
  3. /* By algebraic identity:
  4. x³+y³+3xy(x+y)=(x+y)³
  5. => x³+y³ = (x+y)³-3xy(x+y) */
  6. = [(a+b)³+c³]-3ab(a+b)-3abc.
  7. =[(a+b+c)³-3(a+b)c(a+b+c)]-3ab(a+b+c)
  8. =(a+b+c)[(a+b+c)²-3(a+b)c-3ab]

Why is a3 b3 c3 3abc?

a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

What is the answer of a3 b3 c3?

a3+b3 + c3 = 3abc.

How do you get a 3 b 3 c 3?

a^3 + b^3 + c^3 = (a+b+c)^2 – 3ab(a+b) – 3bc(b+c) – 3ca(c+a) – 6abc.

Is ABC 0 then prove that a3 b3 c3 3abc?

If (a+b+c)=0, then how can you prove a^3+b^3+c^3=3abc? – Quora. Originally Answered: If a+b+c =0 then prove that a^3+b^3+c^3=3abc? Hence, proved! Hence, proved.

How many numbers satisfy the condition a 3 B 3 C 3 ABC?

There are four such numbers: 153, 370, 371, and 407.

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What is the formula for a3 b3?

a3 + b3 = (a + b) (a2 – ab + b2 ).

How do you factor a3 b3?

The factored form of a3 + b3 is (a + b)(a2 – ab + b2): (a + b)(a2 – ab + b2) = a3 + a2b – a2b – ab2 + ab2 + b3 = a3 – b3. For example, the factored form of 64×3 + 125 (a = 4x, b = 5) is (4x + 5)(16×2 – 20x + 25).

What is the rule for a 3 b 3?

An expression of the form a3 + b3 is called a sum of cubes. The factored form of a3 + b3 is (a + b)(a2 – ab + b2): (a + b)(a2 – ab + b2) = a3 + a2b – a2b – ab2 + ab2 + b3 = a3 – b3. For example, the factored form of 64×3 + 125 (a = 4x, b = 5) is (4x + 5)(16×2 – 20x + 25).

How do I get rid of B^3 and c^3 in this expression?

Ww need a factor that makes our expression 0 when it is 0. If f (a,b,c) is this factor, then f (a,b,c)= 0 put into our expression would make that one also 0. and this should be 0. The simplest way to get rid of b^3 and c^3 is if g (b,c) = -b-c +X where we will fill whatever we need for X later.

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How do you get rid of B^3 and c^3 in calculus?

The simplest way to get rid of b^3 and c^3 is if g (b,c) = -b-c +X where we will fill whatever we need for X later. Which is 0 if X=0. Ww need a factor that makes our expression 0 when it is 0.

What is the formula for a^3+b^3?

Basically a^3-b^3 has many formulae which are also called as identities. 2)a^3+b^3= (a+b)^3-3ab (a+b). Basically a^3-b^3 has many formulae which are also called as identities. 2)a^3+b^3= (a+b)^3-3ab (a+b). =>a^3 + b^3= (a-b) [a^2-ab+b^2] this is explanation of first formula. hope this is helpful.