# How do you find the quotient of (3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y)?

Mar 20, 2017

The remainder is $= 0$ and the quotient is color(red)(=3x+4y

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a}$color(red)(3x+4y
$\textcolor{w h i t e}{a a a a a a}$$- - - - -$
$\textcolor{w h i t e}{a a a a a}$$|$$3 {x}^{2} + 7 x y + 4 {y}^{2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$3 {x}^{2} + 3 x y$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$0 + 4 x y + 4 {y}^{2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a}$$4 x y + 4 {y}^{2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$- - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a}$$0 + 0$

The remainder is $= 0$ and the quotient is color(red)(=3x+4y

Mar 20, 2017

$\text{ The Quotient=} \left(3 x + 4 y\right) .$

#### Explanation:

$\underline{3 {x}^{2} + 4 x y} + \underline{3 x y + 4 {y}^{2}} ,$

$= x \left(3 x + 4 y\right) + y \left(3 x + 4 y\right) ,$

$= \left(3 x + 4 y\right) \left(x + y\right) .$

$\therefore \left(3 {x}^{2} + 4 x y + 3 x y + 4 {y}^{2}\right) \div \left(x + y\right) ,$

$= \frac{3 {x}^{2} + 4 x y + 3 x y + 4 {y}^{2}}{x + y} ,$

$= \frac{\left(3 x + 4 y\right) \left(\cancel{x + y}\right)}{\cancel{x + y}} ,$

$= \left(3 x + 4 y\right) , \text{ is the desired quotient.}$

Enjoy Maths.!