Final answer:
Expressions are simplified using the distributive property, e.g., (-1)(4-c) becomes -4 + c. For the number -22, it belongs to the subsets of integers and rational numbers. An algebraic expression for '6 times the difference of b and p' is 6(b - p), while 5(14-2)^2/2 simplifies to 360, and u+xy evaluates to 98 with given values.
Step-by-step explanation:
Use the Distributive Property to Simplify Expressions
1. For the expression (-1)(4-c), apply the distributive property by multiplying -1 with both 4 and -c, which gives us: -4 + c.
2. To simplify 4(2x - 4), distribute 4 to both 2x and -4: 8x - 16.
3. In the expression (10 + 4y) 1/2, the distributive property does not directly apply because of the multiplication of the whole expression by a fraction. If it's meant to be distributed inside a parenthesis, the expression remains unchanged.
4. The number -22 belongs to the subsets of integers and rational numbers within the real numbers.
5. The algebraic expression for "6 times the difference of b and p" is: 6(b - p).
6. Simplify the expression 5(14-2)^2/2 by first calculating inside the parenthesis (14-2), squaring the result, multiplying by 5, and then dividing by 2: 5(12)^2/2 which simplifies to 5(144)/2, and then 720/2, hence the simplified form is 360.
7. To evaluate u+xy, substitute u with 18, x with 10, and y with 8 and perform the multiplication and addition to get the result: 18 + (10)(8), which equals 18 + 80, resulting in 98.