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

Simplify the following expressions.

(a) \( x^5 \times x^3 \) [1]

(b) \( \dfrac{y^{10}}{y^4} \) [1]

Nova's hint:

These questions use the index laws (also called laws of exponents).

Ask yourself: 'Which index law applies — am I multiplying, dividing, or raising a power to a power?'

For example, \( a^m \times a^n = a^{m+n} \), and \( (a^m)^n = a^{mn} \).

Try to Solve it with Nova?