Question

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

Answer 1

Answer:

To verify: (a+b)^2=a^2+2ab+b^2

Explanation:

Given: a=3 and b=2

verification:

LHS-

(a+b)^2

putting the given values

(3+2)^2

(5)^2

25. (5×5=25)

RHS-

a^2+2ab+b^2

putting the given values

(3)^2+2(3)(2)+(2)^2. (3×3=9) (2×2=4)

9+12+4

25

therefore,LHS=RHS

hence verified

Answer 2

$\huge\mathbb{SOLUTION}}$

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

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