Algebra

New Zealand

Level 6 - NCEA Level 1

Lesson

In this chapter, we will be simplifying linear algebraic expressions.

A linear algebraic expression is made of any combination of terms which are either constant (e.g., $5$5, $78$78) or the product of a constant and variable with a power of $1$1 (e.g., $3x$3`x`, $10y$10`y`).

We will combine the following skills to simplify the expressions:

- addition, subtraction, multiplication, and division of algebraic terms
- expansion of brackets
- order of operations

You may recall the order of operations, which is outlined below.

The Order of Operations

The order of operations when you are simplifying algebraic expressions is:

Step 1: Do operations inside grouping symbols such as parentheses (...), brackets [...] and braces {...}.

Step 2: Expand sets of brackets using the distributive law.

Step 2: Do multiplication and division going from left to right.

Step 3: Do addition and subtraction going from left to right.

Each time we complete one of these steps, we simplify our expression until we reach the most simplified form.

Let's look through some examples so we can see this process in action.

Simplify: $8x-5x\times4$8`x`−5`x`×4

Think: We do multiplication before subtraction.

Do:

$8x-5x\times4$8x−5x×4 |
$=$= | $8x-20x$8x−20x |

$=$= | $-12x$−12x |

Note: There were no grouping symbols in Question 1, so we did not need to complete Steps 1 and 2 of the order of operations.

Simplify $8n^2+5n\times7n$8`n`2+5`n`×7`n`.

Simplify $2n\times6n-12n^2\div4$2`n`×6`n`−12`n`2÷4.

Simplify $\frac{5h+15h}{20h^2\div4h}$5`h`+15`h`20`h`2÷4`h`.

Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns

Apply algebraic procedures in solving problems