MATHEMATICS GRADE 8
ALGEBRAIC TERMS AND EXPRESSIONS
In language the basic building blocks are words like dog, fat, Aristotle, figs, is, eats and so on. These are combined into sentences like The dog is fat and Aritstotle eats figs.
In the same way in algebra we have basic building blocks called terms like 4, ab, x², +, >, = and so on. These are used to make expressions such as 4 > x² and ab = 2.
Terms are one or more symbols that express a single quantity e.g. 4ab³ is only one term even though there are four symbols. But when the symbols are separated by signs such as +,-,<,>, =, ≠ then they are treated as separate terms so a + b = 4 is three terms. Note that when symbols are multiplied or divided they form one term only so 4 x a is the same as 4a and it is one term and ¾ is one term. Another important point to remember is that everything enclosed in a set of brackets is treated as a single term e.g. a + b is two terms, but (a+ b) is one term only.
Expressions with only one term are called monomials, those with two terms are binomials, and those with three terms are called trinomials. Expressions with more than three terms (and sometimes those with more than one term) are called polynomials.
Exercise 1
In each of the following expressions decide how many terms there are. Discuss it among yourselves to reach agreement:
a) 4x²y³; b) ab + 2c; c) 2b = 0; d) 2ab + c = 8; e) 2a(b+c) = 8; f) 2(ab + c) = 8; g) 4x²/2; h) 4x²-y/ 2y-x
Just as words can sometimes be broken down into smaller parts such as prefixes, roots and suffixes e.g. in/com/plete/ly has two prefixes, a root (plete) and a suffix or un/shake/able has a prefix, a root and a suffix, in the same way terms and expressions have different parts.
Exercise 2
On an A4 sheet of blank paper write out the following expression in large print:
3y² + 4 = x
Now use the following words to label the relevant parts of the expression: co-efficient; variable; exponent; constant
We will review your answers on Thursday.