Question

How do you simplify `3(2b-a)-(2a-b)`?

Answer 1

`color(darkblue)(7b-5a)`

Explanation:

Simplify by distributing.

First take `3` and multiply it across the first binomial, which is `2b-a`.

`color(orange)3(color(green)(2b)-color(red)a) = (color(orange)3)(color(green)(2b)) - (color(orange)3)(color(red)a)`

Now simplify.

`color(blue)(6b) - color(blue)(3a)`

At this point, we have simplified as much as possible in the first parentheses. We can move on to the `(2a-b)`.

There is a subtraction sign in between the two binomials, so we can take that and distribute it across as a negative sign. Remember: `x - y = x + -y`.

`color(blue)(6b-3a) - color(purple)(2a+b)`

Now combine like terms.

`color(darkblue)(7b-5a)`