Question

Simplify:
$[{(5z-2)}^2+40z]÷(5z+2)$

Answer 1

To simplify :
$[{(5z-2)}^2+40z]÷(5z+2)$

Using the identity,
$a^2-2ab+b^2={(a-b)}^2$ ,
$[{(5z-2)}^2+40z]$
$=[25z^2-20z+4+40z]$
$=[25z^2+20z+4]$

On factorizing,
$25z^2+20z+4$,
we get,
$25z^2+20z+4$
$={\left(5z\right)}^2+2\times \left(5z\right)\times 2+2^2$

On applying the identity, $a^2+2ab+b^2={(a+b)}^2$,
we get ,
$25z^2+20z+4={(5z+2)}^2$

So,
$\left[\frac{({(5z-2)}^2+40z)}{(5z+2)}\right]=\frac{{(5z+2)}^2}{(5z+2)}=5z+2$