Question

How do you simplify `3ab+2a+3b+4ab-a+4b`?

Answer 1

`a + 7 b (a + 1)`

Explanation:

We have: `3 a b + 2 a + 3 b + 4 a b - a + 4 b`

Let's collect the like terms:

`= (3 a b + 4 a b) + (2 a - a) + (3 b + 4 b)`

`= 7 a b + a + 7 b`

We can factor out a `7 b` to get:

`= a + 7 b (a + 1)`

Answer 2

`a+7ab+7b`

Explanation:

`color(red)(+3ab)color(blue)(+2a)color(lime)(+3b)color(red)(+4ab)color(blue)(-a)color(lime)(+4b) " "larr` identify the like terms.

Re-arrange the terms if you prefer to. Make sure the signs stay with the correct terms.

`color(blue)(+2a)color(blue)(-a)color(red)(+3ab)color(red)(+4ab)color(lime)(+3b)color(lime)(+4b)`

Now add the co-efficients, but keep the variables and the powers the same.

`color(blue)(a)color(red)(+7ab)color(lime)(+7b)`