Expressions

Expressions are groups of letters separated by + or – signs.

3p + 2t is an expression.

3p and 2t are called terms.

Like terms are the same letters.

Rules for Addition and Subtraction

Expressions can be simplified by adding or subtracting ‘like terms' only.

See how the following expressions can be simplified:

t + t + t = 3t
3t – t = 2t
4p + 3p = 7p
pq + pq = 2pq
q² + q² = 2q²

These all have ‘like terms' and can therefore be simplified (note: the powers must also be the same).

The expressions below do not have like terms and so cannot be simplified:

3y + 2t = 3y + 2t
4y + 3 = 4y + 3
y² + y³ = y² + y³
5x – 3y = 5x – 3y

This can be applied to more difficult expressions, as in the following examples.

Example 1: Simplify 3t + 4p + 2t – 3p.

3t + 2t = 5t (note: a term has a sign ‘in front of it' which must stay with it)

4p – 3p = p

Therefore 3t + 4p + 2t – 3p = 5t + p.

Example 2: Simplify 5y + 6x – 3y – 8x.

5y – 3y = 2y

6x – 8x = –2x

Therefore 5y + 6x – 3y – 8x = 2y – 2x.

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Note: This can be achieved by simply adding the powers as follows.

b. Unlike terms

See how the following expressions have been simplified:

p x q = pq  (note: we leave out the times sign)

3p x 2q = 6pq (multiply the numbers first and then the letters)

p² x q³ = p² q³

5 x q = 5q

Rules for multiplying in algebra

Rule 1: For ‘like terms' we add the powers.

Rule 2: For ‘unlike terms' we leave out the multiply sign.

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