Question

$x^2$ - $(100\times (y+z{)}^2)÷(x-10y-10z)$

• A. $x+10\times (y+z)$
• B. $x+10\times (y+z)$
• C. $x+100\times (y+z)$
• D. $x+10\times \left(y\right)+10\times \left(z\right)$

Answer 1

Answer: (A), (D)

The correct options are
A $x+10\times (y+z)$
D $x+10\times \left(y\right)+10\times \left(z\right)$

$x^2$ - 100$(y+z{)}^2$ can also be written as $x^2$- ${10}^2$$(y+z{)}^2$.
This is of the form $a^2$ - $b^2$
$a^2$ - $b^2$ = (a+b)(a-b)
$\therefore$ $x^2$- ${10}^2$$(y+z{)}^2$
= (x+ 10(y+z)) (x- 10(y+z))
To solve:

$x^2$ - $(100\times (y+z{)}^2)÷(x-10y-10z)$
$=(x+10(y+z\left)\right)(x-10(y+z\left)\right)÷(x-10y-10z)$
$=(x+10y+10z)(x-10y-10z))÷(x-10y-10z)$
$=(x+10y+10z)=x+10\times (y+z)$