To factor the expression \(40 + 64\), we first need to find the greatest common factor (GCF) of the numbers 40 and 64.
The prime factorization of 40 is: \[ 40 = 2^3 \times 5 \]
The prime factorization of 64 is: \[ 64 = 2^6 \]
To find the GCF, we take the lowest power of each common prime factor. The only prime factor common to both numbers is 2. The lowest power of 2 in the two factorizations is \(2^3\).
Thus, the GCF of 40 and 64 is: \[ \text{GCF} = 2^3 = 8 \]
Next, we factor \(40 + 64\) using this GCF. We can express both numbers in terms of the GCF:
\[ 40 = 8 \times 5 \quad \text{and} \quad 64 = 8 \times 8 \]
Now we rewrite the expression \(40 + 64\): \[ 40 + 64 = 8 \times 5 + 8 \times 8 \] Factoring out the GCF (8): \[ 40 + 64 = 8(5 + 8) \]
Now we simplify the expression inside the parentheses: \[ 5 + 8 = 13 \]
Thus, we have: \[ 40 + 64 = 8(13) \]
Putting it all together, we write the final factored form: \[ 40 + 64 = 8(5 + 8) = 8(13) \]
In summary, the answer in the form \(a(b + c)\) is: \[ \boxed{8(5 + 8)} \]