To find the first difference given the second and third terms, follow these steps:
1. Identify the given terms:
- The second term is given by [tex]\( 3a + 5 \)[/tex].
- The third term is given by [tex]\( 8a - 3 \)[/tex].
2. The first difference is calculated by subtracting the second term from the third term. This can be expressed as:
[tex]\[
\text{First difference} = (\text{Third term}) - (\text{Second term})
\][/tex]
3. Substitute the given terms into the equation:
[tex]\[
\text{First difference} = (8a - 3) - (3a + 5)
\][/tex]
4. Simplify the expression by distributing and combining like terms:
[tex]\[
\text{First difference} = 8a - 3 - 3a - 5
\][/tex]
5. Combine the terms involving [tex]\( a \)[/tex]:
[tex]\[
\text{First difference} = (8a - 3a) + (-3 - 5)
\][/tex]
[tex]\[
\text{First difference} = 5a - 8
\][/tex]
Thus, the first difference is [tex]\( 5a - 8 \)[/tex].
