Sometimes algebraic expressions might involve brackets or parenthesis and addition or subtraction signs inside parenthesis just like 2(x + 4) + 3(x – 5). Such expressions which involve brackets can be re written in equivalent forms without any brackets by applying the distributive property of multiplication over addition. This process is called ‘expanding’ or ‘removing’ brackets

Expanding using the distributive Laws

The distributive law says, for any real numbers a, b and c

2(a + b) = 2a + 2b
3(a − b) = 3a − 3b and
a(b + c) = ab + ac

Note that the left side of the algebraic expressions involve parenthesis and the right sides do not involve parenthesis. However both the left and the right sides are equal. The right side expression is the expanded or distributed form of the left.