Question

$[{(5z-2)}^2+40z]÷(5z+2)$

• A. 2z + 5
• B. 2z - 5
• C. 5z - 2
• D. 5z + 2

Answer 1

The correct option is D

5z + 2

Simplify: [${(5z-2)}^2$ + 40z ]
= [25$z^2$ - 20z + 4 + 40z]
= [25$z^2$ + 20z + 4]
Factorize: 25$z^2$ + 20z + 4
25$z^2$ + 20z + 4 = ${\left(5z\right)}^2$ + 2 $\times$ (5z) $\times$ 2 + $2^2$
$a^2$ + 2ab + $b^2$ = ${(a+b)}^2$
25$z^2$ + 20z + 4 = ${(5z+2)}^2$
$\left[\frac{({(5z-2)}^2+40z)}{(5z+2)}\right]$ = $\frac{{(5z+2)}^2}{(5z+2)}$ = 5z + 2