Draw and explain the polynomial identity: $(x + 4)^{2} = x^{2} + 4^{2} + 8 x$

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Solution

Step 1: Draw a line with a point which divides $x, 4$
Step 2: Total distance of this line $= x + 4$
Step 3: Now we have to find out the square of $x + 4$ i.e., Area of big square, $A B C D =$ $(x + 4)^{2}$
Step 4: From the diagram, inside square red and yellow square, be written as $x^{2}, 4^{2}$
Step 5: The remaining corner side will be calculated as rectangular side $=$ length $\times$ breadth $=$ $x \times 4$
Therefore, Area of the big square, $A B C D =$ Sum of the inside square $+$ $2$ times the corner rectangular side.
$(x + 4)^{2} = x^{2} + 4^{2} + 8 x$
Hence, geometrically we proved the identity $(x + 4)^{2} = x^{2} + 4^{2} + 8 x$ .

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Draw and explain the polynomial identity: (x+4)2=x2+42+8x

Draw and explain the polynomial identity: $(x + 4)^{2} = x^{2} + 4^{2} + 8 x$