Look at the following figure. Justify the identity a² = (a + b)(a - b) + b² for yourself. Class 9

Look at the following figure. Justify the identity a² = (a + b)(a - b) + b² for yourself. Class 9

Question 1.

Look at the following figure. Justify the identity a² = (a + b)(a - b) + b² for yourself. Class 9

Answer:

Consider the original square of side a.

Then, the area of the square is a².

After drawing the dotted lines, the square is divided into :

A rectangle of dimensions a and (a - b).

So, the area of the rectangle is a(a - b).

A rectangle of dimensions b and (a - b).

So, the area of the rectangle is b(a - b).

A small square of side b.

So, the area of the small square is b².

Therefore, total area of the square is a² = a(a - b) + b(a - b) + b²

= (a + b) (a - b) + b²