Algebraic Notation

Grade 3

The shorthand you are already using

Algebraic notation is a set of conventions that let mathematicians write things concisely. Once you know the rules, reading an algebraic expression becomes natural.

Here are the main ones: 3x means 3 × x (the × sign is dropped). ab means a × b. x/y means x ÷ y. x² means x × x. The number in front of a letter is called the coefficient.

Like terms

Like terms are terms that have exactly the same letters raised to exactly the same powers. You can add or subtract like terms — you cannot mix different ones.

3x and 5x are like terms — add them to get 8x. But 3x and 3x² are not like terms, because the powers differ. Leave them as they are.

Worked example — collecting like terms

EXAMPLE

Simplify: 4x + 3y − x + 2y²− 2y

Group like terms: x terms: 4x − x = 3x. y terms: 3y − 2y = y. y² terms: 2y² (nothing to add). Result: 3x + y + 2y².

Substitution

Substitution means replacing a letter with a number. If x = 3 and y = −2, then 2x − y = 2(3) − (−2) = 6 + 2 = 8.

When substituting a negative number, always put it in brackets first. Missing the brackets is the most common arithmetic slip in algebra questions.

Try this one

Work out the value of each expression when \( x = 3 \).

(a) \( x^2 + 7 \) [1]

(b) \( 2x^3 - 10 \) [2]

Nova's hint:

This is about substitution into expressions with indices.

Ask yourself: 'Do I need to apply the power to \( x \) before multiplying by the coefficient?'

For example, if \( x = 2 \), then \( 3x^2 = 3 \times 2^2 = 3 \times 4 = 12 \). Always deal with the power before multiplying.

Try to Solve it with Nova?