Boolean reduction of $AB+(B+C)BC$

Question

Reduce this Boolean expression $$AB+(B+C)BC$$ Please express step by step process to understand clearly.

Answer 1

\begin{align*} AB+(B+C)BC &= AB + B^2C + BC^2\\ & = AB + BC + BC\\ & = AB + BC \end{align*}

Answer 2

Use:

Absorption

$P(P+Q) = P$

With that:

$$AB + (B + C)BC = AB + BC$$ ($B$ absorbs $B+C$)

And if you want, you can use Distribution to make that $B(A + C)$