Study notes

Algebra

Using letters to stand for numbers, and the rules for writing, simplifying and evaluating expressions.

Key ideas

A variable is a letter such as $x$ that stands for a number we do not know yet.
A term is a number, a variable, or a product of them: $5$ , $x$ , $3 x$ , $2 x y$ .
Like terms share the same variable part, so they combine: $3 x + 5 x = 8 x$ ; but $3 x + 5 y$ cannot.
To evaluate, substitute the value: if $x = 4$ , then $3 x + 2 = 3 (4) + 2 = 14$ .
Multiplication is written without a sign: $3 \times x = 3 x$ and $x \times x = x^{2}$ .
Expand a bracket by multiplying every term inside: $3 (x + 2) = 3 x + 6$ .

3 (x + 2) = 3 x + 6

- multiply 3 by each part.

Simplify

4 x + 7 - x + 3

Evaluate

2 a + 3 b

when

a = 5

and

b = 2