Question

Simplify the variable expression. $$3 x+2 y-(5 x+2 y)$$

Short answer

The simplified version of the given expression is \(-2x\).

Step-by-step solution

Distribute the Subtraction

Take account of the negative sign in front of the bracket. This means that the sign of each term in the bracket will change when distributed: \(3x+2y-(5x+2y) = 3x+2y-5x-2y\)

Combine Like Terms

Resume the expression by combining like terms, i.e., terms with the same variable. So combine the terms with \(x\) and then with \(y\). The expression becomes: \(3x - 5x + 2y - 2y = -2x + 0\)

Final Simplification

Now the expression can be further simplified. Since any number added with zero remains the same, the final simplified version of the given expression is \(-2x\).