Question

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

Answer 1

`=+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`