(b+c³)²

To expand the expression \((b+c^3)^2\), you can use the formula for the square of a binomial, which is given by:

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

In this case, let \(a = b\) and \(b = c^3\). Plugging these into the formula, we get:

\[ (b + c^3)^2 = b^2 + 2(b)(c^3) + (c^3)^2 \]

Now, let's calculate each term:

1. \(b^2\) remains \(b^2\).
2. \(2(b)(c^3) = 2bc^3\).
3. \((c^3)^2 = c^6\).

Putting it all together, the expanded form of \((b+c^3)^2\) is:

\[ b^2 + 2bc^3 + c^6 \]