Which expression is equivalent to
`\left(\frac{1}{2}a+5\right)\left(\frac{3}{2}a+1\right)` ?
To find the equivalent expression, we need to expand the given expression by multiplying each term in the first set of parentheses by each term in the second set of parentheses.
This gives us:
`\left(\frac{1}{2}a+5\right)\left(\frac{3}{2}a+1\right)`
`= \frac{1}{2}a * \frac{3}{2}a + \frac{1}{2}a * 1 + 5 * \frac{3}{2}a + 5 *1`
`= \frac{3}{4}a^2 + \frac{1}{2}a + \frac{15}{2}a + 5`
Now, combine like terms:
`= \frac{3}{4}a^2 + \frac{1}{2}a + \frac{15}{2}a + 5`
`= \frac{3}{4}a^2 + \frac{17}{2}a + 5`
So, the equivalent expression is `\frac{3}{4}a^2 + \frac{17}{2}a + 5`.