In this chapter you will learn how to work with algebraic expressions. You will recap some of the work on factorisation and multiplying out expressions that you learnt in earlier grades. This work will then be extended upon for Grade 10.
Recap of earlier work
The following should be familiar. Examples are given as reminders.
Parts of an expression
Mathematical expressions are just like sentences and their parts have special names. You should be familiar with the following names used to describe the parts of a mathematical expression.
Name
Examples (separated by commas)
term
,
,
,
,
,
expression
,
coefficient
,
,
,
exponent (or index)
,
base
,
,
constant
,
,
,
,
,
variable
,
equation
inequality
binomial
expression with two terms
trinomial
expression with three terms
Product of two binomials
A
binomial is a mathematical expression with two terms, e.g.
and
. If these two binomials are multiplied, the following is the result:
The product of two identical binomials is known as the
square of the binomial and is written as:
If the two terms are
and
then their product is:
This is known as the
difference of two squares .
Factorisation
Factorisation is the opposite of expanding brackets. For example expanding brackets would require
to be written as
. Factorisation would be to start with
and to end up with
. In previous grades, you factorised based on common factors and on difference of squares.
Common factors
Factorising based on common factors relies on there being common factors between your terms. For example,
can be factorised as follows:
Investigation : common factors
Find the highest common factors of the
following pairs of terms:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
Difference of two squares
We have seen that:
Since
[link] is an equation, both sides are always equal. This means that an expression of the form:
can be factorised to
Therefore,
For example,
can be written as
which is a difference of two squares. Therefore, the factors of
are
and
.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
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_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life