Question

Explain the polynomial geometrically: $(6x+5{)}^2=36x^2+5^2+60x$

Answer 1

Step 1: Draw a line with a point which divides $6x,5$
Step 2: Total distance of this line $=6x+5$
Step 3: Now we have to find out the square of $6x+5$ i.e., Area of big square, $ABCD=$ $(6x+5{)}^2$
Step 4: From the diagram, inside square red and yellow square, be written as $36x^2,5^2$
Step 5: The remaining corner side will be calculated as rectangular side $=$ length $\times$ breadth $=$ $6x\times 5$
Therefore, Area of the big square, $ABCD=$ Sum of the inside square $+$ $2$ times the corner rectangular side.
$(6x+5{)}^2=36x^2+5^2+60x$
Hence, geometrically we proved the identity $(6x+5{)}^2=36x^2+5^2+60x$.