area of paper

PLEASE ADD A TITLE TO YOU QUESTION!

You have just found the area of the middle bit

( 10-2x )^2 

You would have to add 4 lots of  x(10-2x)  to make your answer correct.

Look at my diagram and see if you can see this.  

$$\\It\; is\; 100-4x^2\\\\
\mbox {But this is not one of the answers so we need to look some more}\\
100=10^2\\
4x^2=(2x)^2\\
\mbox{So we have a difference of two squares}\\
100-4x^2=(10-2x)(10+2x)\\
\mbox{So the answer is c}\\$$

why it 100 - 4x^2 

Because you had a square peice of paper 10cm * 10cm.  That was 100cm^2

then you cut a square out of each of the 4 corners that was [xcm * xcm]*4 = 4x^2 cm^2

so you were left with  [100-4x²] cm²  of paper   

You need to give this question a title please.

i think by this way 

we have a square piece of paper with side-length 10 cm 

if we cut a small square from each corner the side lenght will be 10-2X ..... then the remaining area will be ( 10-2x )^2 

what is the mistake in my way ?