# Solve the following algebraic expression: [5z-(x+2y)]-[3x-(y-2z)] Greetings.  This algebraic expression (incidentally, what's the difference between an expression and an equation? Answer follows) requires you to see that a negative sign can be interpreted as (-1) and distributed using the Distributive Property of Multiplication.

Using the problem-solving strategy of "Simplify and Solve," we first look to determine...

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Greetings.  This algebraic expression (incidentally, what's the difference between an expression and an equation? Answer follows) requires you to see that a negative sign can be interpreted as (-1) and distributed using the Distributive Property of Multiplication.

Using the problem-solving strategy of "Simplify and Solve," we first look to determine if we can combine similar terms.  Not yet. So, let's address those nasty (-) minus signs.  To eliminate the confusion that they create, shall we change all operation signs to (+) addition signs?  Let's do that:

[5z + -1(x + 2y)] + -1[3x + -1(y + -2z)]

= 5z + -1x + -2y + -1[3x + -1y + 2z]

= 5z + -1x + -2y + -3x + 1y + -2z   Now we combine similar terms

=  -4x + -y + 3z

(Oh yes!  An expression does not include an equal sign, but an equation does include an equal sign).

Approved by eNotes Editorial Team Note:

Many algebra textbooks suggest that variables should written in alphabetical order with decreasing exponents with secondary variables having increasing exponents. For example,

x^2 +2xy + y^2 is proper; however

y^2  + x^2 +2xy  is not.

For the original problem described above, a better answer would be

- 4x - y + 3z

instead of demanding that the first term always be positive.

Approved by eNotes Editorial Team This problem is about moving the minus sign inside the parenthesis so that order of operations is preserved.

[5z-(x+2y)]-[3x-(y-2z)]

5z - x - 2y - (3x - y + 2z)

5z - x - 2y - 3x + y - 2z

3z - 4x - y

Approved by eNotes Editorial Team