Answer:
D. ¼r² + 3r + 5.
Step-by-step explanation:
To find the expression that is equivalent to (½r + 1) (½r + 5), we can use the distributive property of multiplication over addition.
Let's start by multiplying the first term of the first binomial (½r) by both terms in the second binomial:
(½r) * (½r) = ¼r²
(½r) * 5 = 2.5r
Next, we multiply the second term of the first binomial (1) by both terms in the second binomial:
1 * (½r) = ½r
1 * 5 = 5
Now, we can combine the like terms:
¼r² + 2.5r + ½r + 5
To simplify further, we can combine the 2.5r and ½r terms:
¼r² + (2.5r + ½r) + 5
¼r² + 3r + 5
Therefore, the expression that is equivalent to (½r + 1) (½r + 5) is ¼r² + 3r + 5.
So the correct answer is D. ¼r² + 3r + 5.
