Sure, let's simplify the expression step-by-step.
Given the expression:
[tex]\[ 2(2x + 3y) - 5(x - y) \][/tex]
First, we will distribute the constants inside the parentheses.
1. Distribute the 2 in [tex]\( 2(2x + 3y) \)[/tex]:
[tex]\[ 2 \cdot (2x) + 2 \cdot (3y) = 4x + 6y \][/tex]
2. Distribute the -5 in [tex]\( -5(x - y) \)[/tex]:
[tex]\[ -5 \cdot (x) - 5 \cdot (-y) = -5x + 5y \][/tex]
Next, combine the results from both distributions:
[tex]\[ 4x + 6y - 5x + 5y \][/tex]
Now, combine like terms:
1. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 4x - 5x = -x \][/tex]
2. Combine the [tex]\( y \)[/tex] terms:
[tex]\[ 6y + 5y = 11y \][/tex]
Putting it all together, we get the simplified expression:
[tex]\[ -x + 11y \][/tex]
So, the simplified form of the original expression is:
[tex]\[ -x + 11y \][/tex]
