Question

How do you simplify `a + 2c - 5b - c + a - b`?

Answer 1

`a+a+2c-c-5b-b`
=`2a+c-6b`

Answer 2

`color(red)(2a)color(olive)(-6b)color(blue)(+c)`

Explanation:

This is addition of algebraic terms.

In Algebra we may only add terms that are like (the same).

There are 6 terms - we can re-arrange them to have the like terms together. The terms are usually arranged in alphabetical order.

`color(red)(a)color(blue)(+2c)color(olive)(-5b)color(blue)(-c)color(red)(+a)color(olive)(-b)`

= `color(red)(a)color(red)(+a)color(olive)(-5b)color(olive)(-b)color(blue)(+2c)color(blue)(-c)`

We only add the numerical coefficients (the numbers in front of the terms) and keep the variables the same.

= `color(red)(2a)color(olive)(-6b)color(blue)(+c)`

Remember that if no number is written it means there is 1.

`color(red)(a = 1a)`