Algebraic Expressions

2.0 Algebra · 2.1 Algebraic Expressions

Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 2.0 Algebra | Sub-Strand 2.1 Algebraic Expressions (6 lessons)

Lesson objectives

By the end of this sub-strand, you should be able to:

An expression is a piece of algebra with no equals sign, such as 6x + 9. This topic is about tidying expressions up and putting numbers into them.

a) Factorising

Factorising means writing an expression as a product. It is the reverse of expanding.

Look for what divides into every term. In 6x + 9, the number 3 divides both, so 3 comes outside the bracket.

Take out the highest common factor. Taking out 3 from 12x + 18 leaves 3(4x + 6). That is not finished, because 2 still divides both terms inside.

Always check by expanding back. If you do not return to what you started with, something was dropped.

b) Factorising with letters

Letters can be common factors too. In 4xy + 6x, both terms contain x, and 2 divides both numbers. So the common factor is 2x, giving 2x(2y + 3).

c) Algebraic fractions

An algebraic fraction has expressions on the top and bottom. Simplify it by factorising both, then cancelling what appears in both.

You may only cancel factors, never single terms out of a sum. In (x + 2)/2 the 2 on top is part of a sum, so nothing cancels.

That restriction catches many learners. Cancelling across a plus sign is the single most common error in this topic.

d) Substitution

Substituting means replacing each letter with a given number and working the answer out.

Write brackets round each number as you put it in. It keeps multiplication clear and prevents 3a becoming 34 when a is 4.

Follow the usual order afterwards: brackets, then multiply and divide, then add and subtract.

e) A useful check

Substitute the same number into an expression and into your simplified version. Both should give the same answer.

If they differ, the simplification is wrong, and you have found it without waiting for the marks.

f) Where this is used

A formula is an expression waiting for numbers. Working out a wage from hours, or an area from measurements, means substituting into an expression.

Words to know

Algebraic expression -- a combination of numbers, variables, and operations, without an equals sign.
Like terms -- terms that contain exactly the same variable (and power), which can be directly combined.
Factorising -- rewriting an expression as a product by extracting a common factor.
Evaluating -- substituting specific numbers for the variables in an expression to calculate its value.

:::checkpoint Check yourself

Try the exercises below -- on factorising, simplifying, and evaluating algebraic expressions.