Final answer:
To express the given algebraic expressions as a single expression, we combine like terms and simplify each expression. After simplifying individual expressions, we combine them into one single expression. The correct single algebraic expression is most similar to option B: 5a + 4b - s + 7x + y + 4r + 5.
Step-by-step explanation:
The student has asked for help in expressing multiple algebraic expressions as a single expression. In combining like terms and simplifying expressions, we look for terms that can be combined because they have the same variables and exponents.
Starting with 7a + 3b - 2a - 5 + b, we combine like terms to simplify. The terms with 'a' can be combined (7a - 2a = 5a) and the terms with 'b' can be combined (3b + b = 4b). Then, we have 5a + 4b - 5.
Looking at 6x - 2x + 4 + 3y - y, we combine like terms again. The terms with 'x' can be combined (6x - 2x = 4x) and the terms with 'y' (3y - y = 2y), resulting in 4x + 2y + 4.
For 2(2r) - s, this simplifies to 4r - s.
The last expression, 12x - y + 5 - 9x + 1, combines to 3x - y + 6 after combining like terms.
Combining all four simplified expressions, we get: 5a + 4b - 5 + 4x + 2y + 4 + 4r - s + 3x - y + 6. Simplifying this further:
Combine constants: -5 + 4 + 6 = 5
Combine x terms: 4x + 3x = 7x
Combine y terms: 2y - y = y
Thus, our final simplified expression is 5a + 4b - s + 7x + y + 4r + 5, which is most similar to option B.