Proof of (a+b) whole Square Formula in Geometrical Method

 

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-The expansion of the algebraic identity (a + b) whole square can be derived in mathematical form by the geometrical approach. In this method, the concept of the areas of the geometrical shapes squares and rectangles are used in proving the a plus b whole square formula.

A Plus B Whole Square

(a + b)2 formula is one the most commonly used algebraic identity in maths. Let’s learn what is a plus b whole square formula here.
The a + b whole square formula is used to expand the binomial term when squared, and to find the square of the difference between two numbers.

The formula for (a + b)2 can be derived as:

(a + b)2 = (a + b)(a + b)

= (a)(a) + (a)(b) + (b)(a) + (b)(b)

= a2 + 2ab + b2

Therefore, (a + b)2 = a2 + 2ab + b2

A Plus B Whole Square Formula Proof

Let us consider a square whose side length is “a” such that its area is equal to “a square”.

First, consider a square with side “a”.

Its area will be “a2”.

Now, extend the lengths of this square by b units as shown in the below figure such that we get two rectangles and a small square with side b.

Side of the new (big) square = a + b

Area of bigger square = (a + b)2

Area of vertical strip (rectangle) = Length × Breadth = a × b = ab

Area of horizontal strip (rectangle) = Length × Breadth = a × b = ab

Area of smaller square = b2

Area of square with side (a +b) = Area of square with side “a” + Areas of two rectangles + Area of small square.

(a + b)2 = a2 + ab + ab + b2

Therefore, (a + b)2 = a2 + 2ab + b2

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So, Let's End up Here..

In the Next Blog, We will be discussing about (a - b)2

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