Question

Draw and prove the identity: $(4m+3n{)}^2=16m^2+9n^2+24mn$

Answer 1

Step 1: Draw a line with a point which divides $4m,3n$
Step 2: Total distance of this line $=4m+3n$
Step 3: Now we have to find out the square of $4m+3n$ i.e., Area of big square, $ABCD=$ $(4m+3n{)}^2$
Step 4: From the diagram, inside square red and yellow square, be written as $16m^2,9n^2$
Step 5: The remaining corner side will be calculated as rectangular side $=$ length $\times$ breadth $=$ $4m\times 3n$
Therefore, Area of the big square, $ABCD=$ Sum of the inside square $+$ $2$ times the corner rectangular side.
$(4m+3n{)}^2=16m^2+9n^2+24mn$
Hence, geometrically we proved the identity $(4m+3n{)}^2=16m^2+9n^2+24mn$.