Rewrite in simplest terms: 7(f + 4) + 2(3f - 8).

Step-by-step solution

1. 1

   Distribute the 7 across the first bracket. Multiply both terms inside, not just the one containing the variable:

   $7(f+4)=7f+28$

2. 2

   Distribute the 2 across the second bracket, keeping the minus.

   $2(3f-8)=6f-16$

   The coefficient $2$ multiplies the coefficient $3$ to give $6f$; a frequent slip is writing $5f$ by adding the coefficients instead of multiplying them.

3. 3

   Write the expression without brackets.

   $7f+28+6f-16$

4. 4

   Combine the variable terms and the constants separately.

   $7f+6f=13f,\qquad 28-16=12$

   so the simplified expression is $13f+12$. It cannot be reduced further, since $13f$ and $12$ are unlike terms and $13$ and $12$ share no common factor.

5. 5

   Verify with test values. At $f=2$ the original gives $7(6)+2(-2)=42-4=38$, and the simplified form gives $13(2)+12=38\;\checkmark$. At $f=0$ the original gives $28-16=12$ and the simplified form gives $12\;\checkmark$ — the $f=0$ check confirms the constant term specifically.