# (a+b)(a-b)

It’s actually not that difficult to calculate once you know the expansion of the binomial (a+b)(a-b). We can use the distributive law to write it out as: a(a-b) + b(a-b).

## (a-b)^2 formula

Then, we can use FOIL to expand each of the terms in brackets. So, we have: a^2 – ab + ba – b^2. This simplifies to: a^2 – b^2. Therefore, (a+b)(a-b) = a^2 – b^2.

(a+b)(a-b) = a^2 – b^2

This can be proven by expanding the left side of the equation:

(a+b)(a-b) = a^2 + ab – ba – b^2

= a^2 + ba – ab – b^2

= a^2 – (ab – ba) – b^2

= a^2 + 0 – b^2 (since ab = ba)

= a^2 – b^2

## a-b)^2

(a+b)(a-b) = a^2 – b^2.

### ab squared

To see why this is true, let’s take a look at the FOIL method of multiplying binomials. When you use the FOIL method, you multiply the terms in order from left to right: first term, outer term, inner term, last term. So for our equation, we would have (a+b)(a-b), which would give us these products:

aa – ab + ba -bb

= a^2 – ab + ba – b^2

= a^2 – (a*b)