AB+BC

(A+B).(A+C)

$$\overline A $$B+A$$\overline B $$ C

(A+C).B

(a+b)($$\overline A + c$$)(b+c)=(a+b)($$\overline A $$+C)

($$\overline A + \overline B )(A + \overline C )(\overline B + \overline C ) = \overline {(A} \, + \overline B )(A + \overline C )$$

$$(A + B)(\overline A + C)(B + C) = (\overline A + \overline {B)} (A + \overline C )$$

$$\overline A \,\overline B + A\,\overline C + \overline B \,\overline C = \,\overline A \overline B + A\,\overline C $$

3

4

5

6