# How do you simplify -(4y-x)-2(2x-5y)?

Nov 6, 2016

$= + 6 y - 3 x$

#### Explanation:

Simplifying this algebraic expression is expanding it by applying distributive property then adding similar monomials .

First:
Distributive Property where a,c and d are integers :

$\textcolor{red}{a} \left(c x + \mathrm{dy}\right) = \left(\textcolor{red}{a} \times c x\right) + \left(\textcolor{red}{a} \times \mathrm{dy}\right)$

Multiplying two integers with same sign results a positive product.

EXAMPLE:

$\textcolor{b r o w n}{- 2 \times - 5 = + 10}$

Mltiplying two integers with different sign results a negative product.

EXAMPLE:

color(brown)( -2 xx +5 = - 10
$\text{ }$

Second:
Arrange similar monomials ,in other words , the monomials having the same variable .

Example:

In the given monomials
$x , + 3 y , - y , z , - 7 x$

Similar monomials are:
$x , - 7 x$

$+ 3 y , - y$
$\text{ }$
$\text{ }$

Applying the Distributive property on the given expression:

$- \left(4 y - x\right) - 2 \left(2 x - 5 y\right)$

$= \textcolor{red}{- 1} \left(4 y - x\right) + \textcolor{red}{\left(- 2\right)} \left(2 x - 5 y\right)$

$= \left(- 1 \times 4 y\right) + \left(- 1 \times - x\right) + \left(- 2 \times 2 x\right) + \left(- 2 \times - 5 y\right)$

$= - 4 y + x - 4 x + 10 y$

$= - 4 y + 10 y + x - 4 x$

$= + 6 y - 3 x$