Question

verify a3+b3 by an activity

Answer 1

Do you mean \[a^{3} + b^{3}\]

Answer 2

what do u mean by activity
and
a3+b3 =(a+b)(a2+b2-ab)

Answer 3

We know that:
\[(a + b)^3 = a^3 + b^3 + 3ab(a + b)\]

So, from this let us try to evaluate the value of a^3 + b^3 i.e,

\[a^3 + b^3 = (a + b)^3 - 3ab(a + b)\]

Solving it further by taking (a + b) common:

\[a^3 + b^3 = (a + b)[(a + b)^2 - 3ab]\]

\[a^3 + b^3 = (a + b)[a^2 + b^2 + 2ab - 3ab]\]

Therefore, the desired value is:

\[a^3 + b^3 = (a + b)[a^2 + b^2 - ab]\]

That is how you can prove it...