ما رأيكم هل هناك تفسير هندسي ل(A + B) ^ 2 = A ^ 2 +2 AB + B ^ 2؟/What do you think is there a geometrical explanation for (A+B)^2=A^2+2AB+B^2?

this is an algebraic equation and has no relationship to geometry

Draw a line equal to A + B (if A=5" and B=2" then draw5 +2 =7" line).
Draw the square of A + B (the square of7" line=49 square inches).
Draw the square of5'' segment (the square of5" line=25 square inches), and extend the sides to meet the sides of the A + B square.
You will see two squares and two rectangles.
Enter the areas of the squares (A^2 , B^2) and rectangles (AB, AB) in the diagram.
If you add these up then you will get A^2 + B^2 +2AB which is equal to the whole line square (A + B)^2 = (A+B)^2=A^2+2AB+B^2 ____________ AB B² ____________ A² AB ____________

The geometrical represention is as follows Draw a square with sides of length A+B.
Draw dotted lines to separate the square into two squares and two rectangles along the length A and B.
The area of the two squares are A^2 and B^2 respectively.
The area of the two rectangles are AB and AB respectively.
Adding the four areas we get the area of the square as A^2 +2AB+B^2 ------(1) But area of the square with sides A+B = (A+B)^2 ------(2) From (1) and (2), (A+B)^2= A^2 +2AB+B^2

of course there is

This identity says: Always each square can be divided into two squares and two identical rectangles نلاحظ أن نقطة تلاقي الأشكال الهندسية الأربعة تقع على أحد قطري المريع الأصلي الذي طول ضلعه يساوي A+B و عندما تنطبق على مركز المربع تكون لدينا حالة المربعات الأربعة المتطابقة المعروفة.

Why (a+b)2 = a2+b2+2ab ? Ever wondered how was the above formula derived? Probably the answer would be yes and is simple.
Everybody knows it and when you multiply (a+b) with (a+b) you will get a plus b whole square.
(a+b) * (a+b) = a2 +ab + ba + b2 = a2 +2ab + b2 But how did this equation a plus b whole square became generalized.
Let’s prove this formula geometrically.( Please refer to the pictures on the side) • Consider a line segment.
• Consider any arbitrary point on the line segment and name the first part as ‘a’ and the second part as ‘b’.
Please refer to fig a.
• So the length of the line segment in fig a is now (a+b).
• Now, let’s draw a square having length (a+b).
Please refer to fig b.
• Let’s extend the arbitrary point to other sides of the square and draw lines joining the points on the opposite side.
Please refer to fib b.
• As we see, the square has been divided into four parts (1,2,3,4) as seen in fig b.
• The next step is to calculate the area of the square having length (a+b).
• As per fig b , to calculate the area of the square : we need to calculate the area's of parts1,2,3,4 and sum up.
• Calculation : Please refer to fig c.
Area of part1 : Part1 is a square of length a.
Therefore area of part1 = a2 ---------------------------- (i) Area of part2 : Part2 is a rectangle of length : b and width : a Therefore area of part2 = length * breadth = ba -------------------------(ii) Area of part3: Part3 is a rectangle of length: b and width : a Therefore area of part3 = length * breadth = ba --------------------------(iii) Area of part4: Part4 is a square of length : b Therefore area of part4 = b2 ----------------------------(iv) So, Area of square of length (a+b) = (a+b)2 = (i) + (ii) + (iii) + (iv) Therefore : (a+b)2 = a2 + ba + ba +b2 i.e.
(a+b)2 = a2 +2ab + b2