How do you factor ab + 4 + a + 4b?

Mar 16, 2018

Group it together
$a b + a + 4 + 4 b$
As you must have noticed by now..... it is the only way
$a b + a = a \left(b + 1\right)$
$4 + 4 b = 4 \left(b + 1\right)$
Put them together
$a \left(b + 1\right) + 4 \left(b + 1\right)$
$\left(a + 4\right) \left(b + 1\right)$

Mar 16, 2018

$\left(a + 4\right) \left(b + 1\right)$

Explanation:

$a b + 4 + a + 4 b$

$\implies a b + a + 4 b + 4$

$\implies a \left(b + 1\right) + 4 \left(b + 1\right)$

$\implies \left(a + 4\right) \left(b + 1\right)$