Overview
The distributive property preserves a product by multiplying every term inside a group. Like terms can then combine because they share the same variable factors. A subtraction before parentheses is multiplication by −1, so it reverses every sign in that group.
Consider this example: Simplify 4(2x − 3) − 5x. Distribute 4 to both terms: 8x − 12 − 5x. Combining like terms gives 3x − 12. The option 3x − 3 multiplies 2x but leaves the constant unmultiplied.
The method also handles a different case: Simplify 3x − (2x − 7) + 4. Subtracting the group gives −2x + 7. Then 3x − 2x + 7 + 4 = x + 11. The result x − 3 comes from failing to reverse the sign of −7.
For a further application, consider: Expand and simplify −(x − 2) + 2[3 − (x + 1)]. The first group becomes −x + 2. Inside the bracket, 3 − x − 1 = 2 − x, so doubling gives 4 − 2x. Adding produces −3x + 6. Keeping a positive x in the inner subtraction leads to x + 6.
Changing only the first sign when subtracting a group leaves the remaining terms incorrect. Unlike powers cannot be merged merely because they use the same letter. Expand one group at a time and collect like terms by degree. On a new problem, test the original and simplified expressions at a convenient input as a quick check; that check supports but does not replace algebra.