Question

Verify the identity (a+b)^2= a^2+2ab+b^2 geometrically by taking a=3 and b=2

Answer 1

$\huge\mathbb{SOLUTION}}$

$\bold{(a+b)^2=a^2+2ab+b^2}}$

Draw a square with the side a+b,I,e 3+2

L.H.S area of whole square

$\large\bold{=(3+2)^2=5^2=25}$

R.H.S. = area of square with 3units + area of square with side 2 units + area of rectangle with sides 3,2units+area of rectangle with sides 2,3 units

$\large\bold{=3^2+2^2+3*2+3*2}$

$\large\bold{=9+4+6+6=25}$

$\large\bold{l.h.s=r.h.s}$

Therefore hence the identity is verified

Answer 2

Explanation:

(a+b)²= a²+2ab+b² (So u know that's equal already)

ALGEBRAIC

(3+2)²= 3²+2(3*2)+2²

Expand the identity

3²+2(3*2)+2²=3²+2(3*2)+2²

=9+12+4=9+12+4

=25=25

LHS = RHS

THUS PROVED

GEOMETRICAL

(I have taken the given measurements)

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