Question

Verify the identity ${(a+b)}^2\equiv a^2+2ab+b^2$ geometrically by taking $a=3$ and $b=2$

Answer 1

${(a+b)}^2\equiv a^2+2ab+b^2$
Draw a square with side $a+b$ ie $3+2$
LHS Area of whole square
$={(3+2)}^2=5^2=25$
RHS $=$ Area of square with side $3$ units + Area of square with side $3$ units + Area of rectangle with side $3,2$ units + Area of rectangle with side $2,3$ units
$=3^2+2^2+3\times 2+3\times 2$
$=9+4+6+6=25$
LHS=RHS.
Hence verified.