Question

(a-b)^2=a^2-2ab+b^2


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Answer 1

Answer:

(a-b)²=a²-b (a-b)- b (a-b) -b²

= a²- ab + b²-ab +b²-b²

=a²-2ab+b²

hence, geometrically we proved the indentify (a-b)=a²-2ab+b²

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Step 1: Draw a square ACDF with AC=a units.

Step 2: Cut AB=b units so that BC=(a−b) unts.

Step 3: Complete the squares and rectangle as shown in the diagram.

Step 4: Area of yellow square IDEO= Area of square ACDF− Area of rectangle GOFE− Area of rectangle BCIO− Area of red square ABOG

Therefore, (a−b)

2

=a

2

−b(a−b)−b(a−b)−b

2

= a

2

−ab+b

2

−ab+b

2

−b

2

= a

2

−2ab+b

2

Hence, geometrically we proved the identity (a−b)

2

=a

2

−2ab+b

2

.