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
.
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product