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整式 Integral Expression - Coggle Diagram
整式
Integral Expression
Chp.1 - 整式的概念
9.1 - 字母表示数
(Variables & Expressions)
🔤 using letters to represent specific numbers
✍🏻 e.g. a+b = b+a (b is a rational number)
e.g. (2) S= 1/2 ah (formula of triangle area
⚠️ always write the number in front of the letter
(e.g. a multiply by two - 2a, not a2)
9.2 - 代数式
(Algebraic Expression)
📖 definition - an expression built up from
constants, variable, and the algebraic operations
by an exponent that is a
rational number
⚠️ a single
number
or
letter
is also an algebraic expression
✍🏻 counter - examples (not algebraic expressions): x=1, x>1
9.3 - 代数式的值
(The Value of Algebraic Expression)
📖 definition - substitute the letters in the algebraic expression with
numbers
, and calculate the result
✍🏻 e.g. 100 is the result of the expression n² (the square of n) when n=10 or when n=-10
⚠️ sometimes, there can be
more than one value
to one letter
9.4 - 整式
(Integral Expression)
monomial (单项式)
📖 definition - a
product of a number
and one or more variable with
non - negative
integer exponents
✍🏻 special examples: 1/2, a, π
coefficient (系数):
numerical factor
degree (次数):
sum of the exponents
of its variables
⚠️ the degree of a
non - zero constant
is
zero
polynomial (多项式)
📖 definition - a
sum
of
monomials
term (项): a single
number
/
variable
/ numbers and variables
added
together
📑 vocabulary (term): binomial - 二项式, trinomial - 三项式, polynomial in four terms (or above) - 四项式（及以上）
degree of a polynomial (多项式的次数): the
greatest degree
of any term in the polynomial
📑 vocabulary (degree): linear - 一次, quadratic - 两次, cubic - 三次, quartic - 四次, quintic - 五次, sixth degree (and above) - 六次（及以上）
Chp. 3 - 整式的乘法
Chp. 2 - 整式的加减
9.5 - 合并同类项
(Combining Like Terms)
📖 definition (like terms) - terms with exactly the same
variable form
⚠️ all
constant terms
are like terms
✍🏻 e.g. a and b, 0 and 1, 4a²b²c and 18a²cb²
⚙️ how to combine like terms
Step 1:
find
like terms
Step 2:
move
the like terms together
Step 3:
combine
the like terms
e.g. (how to combine like terms):
4a²b²c + 18a²cb² = 24a²b²c
9.6 - 整式的加减
(Adding and Subtracting Integral Expressions)
⚠️ when the symbol before the bracket is a
plus (+)
, directly remove the bracket
without changing anything
⚠️ when the symbol before the bracket is a
minus (-)
, remove the bracket, and
change the symbol of every term
in the bracket
✍🏻 e.g. x+(y+z) = x+y+z
x-(y+z) = x-y-z