Sure, let's solve the expression step-by-step:
The given expression is:
[tex]\[ 3(x + y) - 2(x - y) \][/tex]
1. Distribute the constants inside the parentheses:
[tex]\[ 3(x + y) \][/tex] becomes [tex]\[ 3x + 3y \][/tex]
[tex]\[ -2(x - y) \][/tex] becomes [tex]\[ -2x + 2y \][/tex] (be careful with the signs here)
2. Combine the two parts:
Now add the results from step 1:
[tex]\[ 3x + 3y - 2x + 2y \][/tex]
3. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( 3x - 2x = x \)[/tex]
- Combine the [tex]\( y \)[/tex] terms: [tex]\( 3y + 2y = 5y \)[/tex]
4. Write the simplified expression:
Putting it all together, we get:
[tex]\[ x + 5y \][/tex]
So, the simplified form of the expression [tex]\( 3(x + y) - 2(x - y) \)[/tex] is [tex]\( x + 5y \)[/tex].
