Question

To prove Ca-b]²
a² 2ab + b² by using
algebra tiles​

Answer 1

Fourthly, when drawing a horizontal and vertical line from intersecting points (b), we gets two squares which has a different area, called as A1, A4 and two rectangles called as A2, A3,in addition, the area of the rectangles A2 and A3 are same. On other word, we can say that the area of a square (A) is equal to sum of the area of two squares (A1,A4) and two rectangles(A2, A3).

A=A1+A2+A3+A4 —————————- (1)

Fifthly, calculate the area of squares and rectangles,

Area of a square A=a²

Area of big square A1 = (a-b)²

Area of a rectangle A2=b (a-b) =ab-b²

Area of a rectangle A3 = b (a-b) =ab-b²

Area of a small square A4= b²

Sixthly, while applying these above areas to equation 1, we can get the result as follow,

A= A1+A2+A3+A4

a²= (a-b) ²+ (ab-b²) + (ab-b²) +b²

a²= (a-b) ²+ab-b²+ab-b²+b²

a²= (a-b) ²+2ab-2b²+b²

a²= (a-b) ² +2ab-b²

Finally, rearrange the above equation,

(a-b)² = a²+b²-2ab

Hence, we have proved by geometrically.

Proof of (a-b)²=a²+b²-2ab by Numerical method: