Question

What is the formula for acube+b cube +c cube

Answer 1

3ab+3bc+3ca-3ab(a+b)-3bc(b+c)-3ac(a+c)-6abc

Answer 2

Answer:

The formulas are

$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)+3abc$

$a^3+b^3+c^3=(a+b+c)^3-(a+b+c)(ab+bc+ca)$

Step-by-step explanation:

we have to find the formula for

$a^3+b^3+c^3$

The identity for the above are

$a^3+b^3+c^{3}-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

which can be written as

$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)+3abc$

Also in other way

$(a+b+c)^3=a^3+b^3+c^3+(a+b+c)(ab+bc+ca)$

⇒ $a^3+b^3+c^3=(a+b+c)^3-(a+b+c)(ab+bc+ca)$

which are the required formulas for $a^3+b^3+c^3$