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

1 Answer
Nov 6, 2016

Answer:

#=+6y-3x#

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 :

#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 #
#" " #

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 #
#" "#
#" "#

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#