Question

what is the formula of a square minus b square
$a2 - b2$

Answer 1

a2-b2=(a+b)(a-b).

Let's prove this by opening the brackets:

a2-b2=a*a+a*-b+b*a+b*-b.
a2-b2=a2-ab+ba-b2.

ab is the same as ba:

a2-b2=a2-ab+ab-b2.

ab and ba get cancelled:

a2-b2=a2-b2.

Hence proved that the identity a2-b2=(a+b)(a-b).

Answer 2

Given:

$a^{2} -b^{2}$

To Find:

The formula for the given equation

Solution:

The formula for $a^{2} -b^{2}$ is (a+b)(a-b)

we can also prove this equation by taking the reverse value

$=(a+b)(a-b)\\=a^2-ab+ba-b^2\\=a^2-b^2$

First to open the bracket multiply it as a(a-b) then add it to b(a-b) then we get -ab and +ba because ab is the same as ba we subtract both of them then we get the proof of the formula.

Hence, the formula will be (a+b)(a-b).

Extra:

$a^3+b^3=(a+b)(a^2+b^2-ab)\\a^3-b^3=(a-b)(a^2+b^2+ab)$