Question

what expression is equivalent to (1/2a+5)(3/2a+1)

Answer 1

To find an expression equivalent to \((\frac{1}{2}a + 5)(\frac{3}{2}a + 1)\), we will use the distributive property (also known as the FOIL method for binomials) to expand the expression.

1. **First**: Multiply the first terms:
\[
\frac{1}{2}a \cdot \frac{3}{2}a = \frac{3}{4}a^2
\]

2. **Outer**: Multiply the outer terms:
\[
\frac{1}{2}a \cdot 1 = \frac{1}{2}a
\]

3. **Inner**: Multiply the inner terms:
\[
5 \cdot \frac{3}{2}a = \frac{15}{2}a
\]

4. **Last**: Multiply the last terms:
\[
5 \cdot 1 = 5
\]

Now, combine all these results:
\[
\frac{3}{4}a^2 + \frac{1}{2}a + \frac{15}{2}a + 5
\]

Next, combine the \(a\) terms:
\[
\frac{1}{2}a + \frac{15}{2}a = \frac{16}{2}a = 8a
\]

Thus, the combined expression is:
\[
\frac{3}{4}a^2 + 8a + 5
\]

Therefore, the expression equivalent to \((\frac{1}{2}a + 5)(\frac{3}{2}a + 1)\) is:
\[
\frac{3}{4}a^2 + 8a + 5
\]