Final answer:
The expression 4(3z+7)+5(8+6z) simplifies to 42z + 68, and due to lack of common factors, this expression cannot be factored further beyond 1(42z + 68) which is equivalent to the simplified form.
Step-by-step explanation:
The student's question requires us to first simplify the expression and then factor it if possible. The expression given is 4(3z+7)+5(8+6z). To simplify, we distribute the multiplication:
- Multiply 4 by both terms inside the first parentheses: 4 × 3z = 12z and 4 × 7 = 28.
- Multiply 5 by both terms inside the second parentheses: 5 × 8 = 40 and 5 × 6z = 30z.
- Combine like terms: 12z + 28 + 40 + 30z.
Adding together the like terms (12z and 30z; 28 and 40) gives us 42z + 68.
To check if our simplified expression is reasonable, we look at the coefficients and constants to ensure arithmetic has been performed correctly. Since we have no common factors other than 1 for 42z and 68, factoring this expression would only give us 1(42z + 68), which is effectively the same as the simplified expression.