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Algebra
the part of mathematics in which letters and other symbols are used to represent numbers and quantities in formulae and equations.
when you take something unknown and represent it with an alphabet or shape so that it is easier to solve, with or without knowing the actual value.
Is
In Algebra,
An expression is a mathematic phrase with numbers and/or variables using mathematical operations. It does not contain an equal sign.
E.g 10x + 4
5y + 8x
An equation asserts the equality of two expression.
E.g 10x + 4 = 24
5y + 8x = 31
A fomula solves a variable.
E.g 10x + 4 = 24
10x = 20
x = 2
It is
an expression where there is an unknown factor that is represented by a symbol.
using letters to represent the unknown numbers in an equation or formula.
Thank You
Done By Sylvia Soh
Factorisation
S2-09
Factorisation of Quadratic Expressions
Variable
13a + 8b + 8
Multiplication Property
There is no change in an inequality if both sides of the inequality are multiplied by the same positive real number.
The process of writing a algebraic expression as a product of its factors.
It is a symbol for a number we do not know yet, for example x or y.
= is equal to
< is less than
> is greater than
< is less than or equal to
> is greater than or equal to
Alphabets are mostly used
Trial and error method known as “cross method” is used to factorise quadratic polynomial.
If a < b and c > 0 , then ac < bc
Common Factors
Grouping
Cross Method
E.g
3 < x > 6 means x is bigger than 3 and 6
3 < x < 4 means x is bigger than 3 but smaller than 4
is used if there is no common factor in an expression. The terms are arranged into groups such that there is a common factor in each group then factorised by using the common factor.
Division Property
There is no change in an inequality if both
sides of the inequality are divided by the same positive real number.
Constant
13a + 8b + 8
Coefficient
Inequality
If a < b and c > 0 , then a/c < b/c
Algebraic Identities
13a + 8b + 8
A number standing on it's own
(a+b)²=a²+2ab+b²
It is a number used to multiple its variable.
Example: 1, 8.5, 100
(a-b)²=a²-2ab+b²
Note that the middle term is obtained by cross-multiplying the factors of the 1st term, and constant term. The order of the factors is important.
(a+b)(a-b)=a²-b²
Expansion
It is like removing the brackets in an algebraic expression and expanding it.
Expansion of algebraic expression using distributive law:
a(b + c) = ab + ac
(a+b)(c+d) = a(c+d) + b(c+d)
= ac + ad + bc+ bd
Expansion of Bracketed Terms using Formula:
(a+b)²=a²+2ab+b²
(a-b)²=a²-2ab+b²
(a+b)(a-b)=a²-b²