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

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Answer 1 · 2016-11-06T06:00:13

$=+6y-3x$

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 :

$color(red)a(cx + dy)=(color(red)axxcx)+ (color(red)axxdy)$

Multiplying two integers with same sign results a positive product.

EXAMPLE:

$color(brown)( -2 xx -5 = +10)$

Mltiplying two integers with different sign results a negative product.

EXAMPLE:

$color(brown)( -2 xx +5 = - 10$
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Second:
Arrange similar monomials ,in other words , the monomials having the same variable .

Example:

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

Similar monomials are:
$x , -7x$

$+3y, -y$
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Applying the Distributive property on the given expression:

$-( 4y - x)-2( 2x - 5y )$

$=color(red)(-1)( 4y - x )+color(red)((-2))(2x - 5y)$

$=(-1xx4y)+(-1xx-x)+(-2xx2x)+(-2xx-5y)$

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

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

$=+6y-3x$

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