Question

verify the algebrice identity (a+b) 2 =a2 +2ab + b2​

Answer 1

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Area of the square PQRS on the white sheet paper.

(a+b)² = (4+2)² = 6 x 6 = 36 sq. units ……….(i)

Area of two coloured squares I and II

area of Ist square = a² = 42 = 16 sq.units

area of IInd square = b² = 22 = 4 sq.units

Area of two coloured rectangles III and IV = 2(a x b) = 2(4 x 2) = 16 sq. units

Now, total area of four quadrilaterals (calculated)

= a²+ b² + 2(ab)

= 16+4+16

= 36 sq. units ……….(ii)

Area of square ABCD = Total area of four quadrilaterals = 36 sq. units

Equating (i) and (ii)

Area of square PQRS = Area of square ABCD

i.e., (a+b)² = a² + b² + 2ab

Algebraic identity (a+b)² = a² + 2ab + b² is verified.

Answer 2

Answer:

L. H. S

(a+b) *(a+b) =a(a+b)+b(a+b)

=a^2+ab+ab+b^2

=a^2+2ab+b^2=R.H.S

HENCE PROVED