Question

Draw the geometrical figure for the identities. (x+y) whole square = x square + 2xy + y square ​

Answer 1

$\huge\rm\red{ANSWER:}$

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 parts 1,2,3,4 and sum up.

Calculation : Please refer to fig c.

Area of part 1:

Part 1 is a square of length a.

∴ area of part 1=a²

------- (i)

Area of part 2:

Part 2 is a rectangle of length :b and width :a

∴ area of part 2=length×breadth=ba ----------(ii)

Area of part 3:

Part 3 is a rectangle of length:b and width :a

∴ area of part 3=length×breadth=ba -------------(iii)

Area of part 4:

Part 4 is a square of length :b

∴ area of part 4=b²

--------(iv)

So, Area of square of length (a+b)=(a+b)²

=(i)+(ii)+(iii)+(iv)

∴(a+b)²

=a²+ba+ba+b²

i.e. (a+b) ²

=a²+2ab+b²

Hence Proved