Final answer:
The simplification of the algebraic expressions results in 3y - 11, 3, -2x + 11, and m² + 10m + 25, using rules of algebra and pertinent operations such as combining like terms, distributing, and FOIL.
Step-by-step explanation:
To simplify the following expressions, we'll follow the rules of algebra and the order of operations.
For the expression 6y - 9 - 3y - 2, we combine like terms:
The simplified expression is 3y - 11.
For the expression 6ab ÷ 2ab, we divide the coefficients and cancel the common variables:
- 6 / 2 = 3
- ab/ab is 1 since any number divided by itself is 1.
The simplified expression is 3.
For the expression 5 - 2(x - 3), we distribute the -2:
The simplified expression is -2x + 11.
Finally, to simplify the expression (m + 5)(m + 5), we apply the FOIL method:
- First: m * m = m²
- Outer: m * 5 = 5m
- Inner: 5 * m = 5m
- Last: 5 * 5 = 25
The simplified expression is m² + 10m + 25.
It's important to eliminate terms wherever possible and check that the simplified expression is reasonable.