When the given expression is factored into the form (a-b)(a^2+ab+b^2) , what is the value of b^2 b^2=square

To factor the given expression $(a-b)(a^{2}+ab+b^{2})$, we need to expand it and compare it with the original expression.<br /><br />Expanding $(a-b)(a^{2}+ab+b^{2})$:<br />$(a-b)(a^{2}+ab+b^{2}) = a(a^{2}+ab+b^{2}) - b(a^{2}+ab+b^{2})$<br />$= a^{3}+a^{2}b+ab^{2} - a^{2}b-ab^{2}-b^{3}$<br />$= a^{3}-b^{3}$<br /><br />Comparing this with the original expression $a^{3}-b^{3}$, we can see that $b^{2}$ is the coefficient of the $ab^{2}$ term in the expanded expression.<br /><br />Therefore, the value of $b^{2}$ is $\boxed{1}$.