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 side of the square PQRS is (x + y).
∴ A(□ PQRS) = (x + y)2

The square PQRS is divided into 4 rectangles: I, II, III, IV

A(□ PQRS) = Sum of areas of rectangles I, II, III, IV.

∴ A (□ PQRS)= A (Rectangle I) + A (Rectangle II) + A (Rectangle III) + A (Rectangle IV)
∴ (x + y)2 = x2 + xy + xy + y2

∴ (x + y)2 = x2 + 2xy + y2

Now, let us multiply (x + y)2 as algebraic expressions.

(x + y) (x + y) = x (x + y) + y (x + y)

(x + y) (x + y) = x2 + xy + yx + y2

∴ (x + y)2 = x2 + 2xy + y2

The expression obtained by squaring the binomial (x + y) is equal to the expression obtained by finding the area of the square.

Therefore, (x + y)2 = x2 + 2xy + y2 is the formula for the expansion of the square of a binomial.

Example

Expand: (2x + 3y)2

(2x + 3y)2

= (2x)2 + 2(2x) x (3y) + (3y)2

= 4x2 + 12xy + 9y2.

Example

Expand: (51)2

(51)2

= (50 + 1)2

= 502 + 2 x 50 x 1 + 1 x 1

= 2500 + 100 + 1

= 2601.

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