Adding and subtracting like terms

curriculum-key-fact
Algebraic terms that have the same letter are called like terms. Only like terms can be added or subtracted.

9b, -7b and 13b are like terms, but 6t, 5x and -11z are not like terms.

When like terms are added and subtracted, it is called simplifying.

Adding and subtracting like terms

The Khan family and the Norman family visit the zoo together - there are {8} children and {7} adults in the group. Because there are more than {10} people, the families can take advantage of a special offer - {1} child can be admitted free of charge.

As before if we use {g} for the cost of child admission and {k} for the cost of adult admission, then:

Cost for the Khan family = 3g + 3k

Cost for the Norman family = 5g + 4k

Offer = - g

Total cost = 3g + 3k + 5g + 4k - g

Simplified = 3g + 5g - g + 3k + 4k = 7g + 7k

+ and - signs

A term, like a number, belongs with the sign that sits in front of it. So in the expression 2k - g, the g belongs with the - sign that sits in front of it, so it is - g. Similarly, 2k belongs with the + sign that sits in front of it, making it + 2k.

Example

Collect all the like terms together for 3g + 3k + 5g + 4k - g.

Gathering all the gs and ks together would give 3g + 5g - g + 3k + 4k.

When you add or subtract terms, keep each term with their + or - sign.

Question

Simplify 4x + y - 2x + 6y

Rewrite the expression by putting the like terms next to each other. Remember to keep the + or - with the terms they belong to.

4x + y - 2x + 6y

= 4x - 2x + y + 6y

Simplify this to get:

2x + 7y