Maharashtra State BoardSSC (English Medium) 7th Standard
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Expansion of (a - b)2 = a2 - 2ab + b2

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formula

(a - b)2 = a2 - 2ab + b2.

notes

Expansion of (a - b)2 = a2 - 2ab + b2:

In the above figure, the square with side a is divided into 4 rectangles,
namely, square with side (a - b), square with side b, and two rectangles of
sides (a - b) and b.

A (square I) + A (rectangle II) + A (rectangle III) + A (square IV) = A (□ PQRS)

(a - b)2 + (a - b)b + (a - b)b + b2 = a2

(a - b)2 + 2ab - 2b2 + b2 = a2

(a - b)2 + 2ab - b= a2

 ∴ (a - b)2 = a2 - 2ab + b2

Let us multiply the algebraic expressions and obtain the formula.
(a - b)2 = (a - b) × (a - b)
(a - b)2 = a (a - b) - b (a - b)
(a - b)2 = a2 - ab - ab + b2
(a - b)2 = a2 - 2ab + b2.

Example

Expand: (5x - 4)2

(5x - 4)2

= (5x)2 - 2(5x) x (4) + 42

= 25x2 - 40x + 16.

Example

Expand: (98)2

(98)2

= (100 - 2)2

= 1002 - 2 x 100 x 2 + 22

= 10000 - 400 + 4

= 9604.

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