The algebraic identities (a – b)² and (a + b)² are the most commonly used algebraic identities in mathematics. These are used in the process of simplifying numerical expressions as well as binomial equations with variables.
In this article, you will understand: the a minus b whole square formula and complete it with supporting evidence and illustrative examples.
A minus B whole square formula
The formula (a – b)² is also generally recognised as the square of the difference between the two variables. This is another common name for the formula. This formula is used in various instances to factorise the binomial.
Let’s become familiar with the formula for the a-minus-b whole square.
(a – b)2 =a2 – 2ab + b2
It is possible to compute the square of the difference between two integers by using the formula (a – b)², which is also used to extend the binomial term when it is squared.
It is important to arrive at the formula for (a – b)² by using the following steps:
(a – b)2 = (a – b)(a – b)
= (a)(a) – (a)(b) – (b)(a) + (b)(b)
= a2 – 2ab + b2
Proof of a minus b whole square formula
Consider a square with side lengths of “a” and an area that may be expressed as “a²” when multiplied together.
Now, create a little square out of this, and make sure that one of its sides has the value (a – b). As a result, we end up with two rectangles, one of which is horizontal and the other of which is vertical.
Let’s total up all the areas of these three different quadrilaterals.
The area of a square whose side is (a – b) is equal to (a – b) square.
The area of the vertical strip (rectangle) may be calculated as follows: Area = Length X Breadth = a X b = ab
The area of the horizontal strip (rectangle) equals length multiplied by width, which equals (a – b) times width, which equals b(a – b).
The area of the square that has the side “a” equals the area of the square that has the side (a – b) plus the areas of the two rectangles.
a2 = (a – b)2 + ab + b(a – b)
a2 = (a – b)2 + ab + ab – b2
a2 = (a – b)2 + 2ab – b2
Therefore, (a – b)2 = a2 – 2ab + b2