Year 7AC9M7A02

Like Terms and Collecting Them

Formulate algebraic expressions using constants, variables, operations and brackets.

You can only add things that are the same kind. Three apples plus two apples is five apples; three apples plus two oranges stays as it is.

Method

Like terms have identical letter parts

3x \text{ and } 7x \text{ are like} \qquad 3x \text{ and } 3y \text{ are not}

Add or subtract the numbers in front only

3x + 7x = 10x

The letter part never changes.

$x$ and $x^2$ are different kinds

x + x^2 \text{ cannot be simplified}

The power is part of the letter part.

e.g.

\text{Simplify } 5a + 3b - 2a + 4b

Underline each kind of term so nothing gets lost. $5a,\ -2a \quad\text{and}\quad 3b,\ 4b$
Take the sign in front of each term with it. $-2a \text{ keeps its minus}$
Collect the first kind. $5a - 2a = 3a$
Collect the second kind. $3b + 4b = 7b$
Write the answer with the terms in alphabetical order. $3a + 7b$

Collect the like terms. Take each sign with its term.

4x + 6x

Answer

10x

9y - 2y + y

Answer

8y

3m + 5n - m + 2n

Answer

2m + 7n

7p - 3q - 7p

Answer

-3q

\text{Why can } 4x + 3x^2 \text{ not be simplified?}

Answer

x \text{ and } x^2 \text{ are different kinds of term.}