Factorize the Expression: Breaking Down 26a + 65bc Step-by-Step

To factor the expression $26a + 65bc$, we start by identifying the greatest common factor of the coefficients:

• The coefficients are 26 and 65.
• The prime factorization of 26 is $2 \times 13$.
• The prime factorization of 65 is $5 \times 13$.
• The greatest common factor of 26 and 65 is 13, because both coefficients are divisible by 13.

Now, factor out $13$ from both terms of the expression:

$26a = 13 \times 2a$

$65bc = 13 \times 5bc$

So, we can express the entire expression as:

$26a + 65bc = 13(2a + 5bc)$

Therefore, the factorized form of the expression is $\mathbf{13(2a + 5bc)}$.

Comparing with the given choices, this corresponds to choice 1.