数学思导
section1
section2
1.7 Multiplying powers with the same base
1.8 Power of a power
1.9 Power of a product
1.6 Addition and subtraction of integral expressions
1.5 Combing Like terms
1.10.2 Multiplying polynomials
1.4 Integral expressions
1.11 The difference of squares formula
1.2&1.3 Algebraic expression & Values of algebraic expressions
1.12 The perfect square formula
1.1 Variables and Expressions
1.10.1 Multiplying monomials, Multiplying monomial and polynomial
1.13 Factorising by extracting CF
1.14.1 Factorising by the difference of squares formula
1.14.2 Factorising by the perfect square formula
1.15 Factorising by cross multiplication（coursework）
1.16 Factorising by grouping
section3
1.17 Division of powers with the same base
1.18 Dividing a monomial by another monomial
1.19 Dividing a polynomial by another monomial
Variables are symbols used to represent unspecified numbers/values.
writing rules
•When a number times a letter, the multiplication sign can be removed. But the number must be put in front.
•If the number is a mixed fraction, it must be turned into an improper fraction.
•Usually a division is written as a fraction.
An algebraic expression is an expression built up from constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
The result calculated according to the operation relationship in the algebraic expression is called the value of the algebraic expression
def
A monomial is a product of a number and one or more variables with non-negative integer exponents. ESP. A number or a variable is also a monomial.
The numerical factor is called coefficient.
The degree of a monomial is the sum of the exponents of its variables.
A polynomial is a sum of monomials.
Monomial and polynomial are called integral expression.
In Algebra a term is either a single number or variable, or numbers and variables multiplied together.
A single number is also called a constant term.
Like terms are terms with exactly the same variable form.
brackets
If a bracket is preceded by a plus sign, remove it by
writing its terms as they are.
If a bracket is preceded by a minus sign, change positive signs within it to negative and vice-versa.
to multiply two powers that have the same base, add their exponents.
a^m · a^n = a^m+n
when raising a power to a power, keep the base and multiply the indices
If 𝑛 is a positive integer (𝑎𝑏)^n = 𝑎^n·b^n
Step1: Multiply all terms of one polynomial by each term of the other polynomial.
Step2: Add all the products.
(𝒂+𝒎) (𝒃+𝒏)
= 𝒂𝒃 + 𝒂𝒏 + 𝒃𝒎 + 𝒎𝒏
Difference of squares formula:
(a+b)(a-b) = a^2 - b^2
𝟐𝒂·𝟑𝒃 =(𝟐×𝟑)(𝒂·𝒃) =𝟔𝒂𝒃
𝟐𝒂·𝟑𝒃 = 𝟔𝒂𝒃
steps of multiplying monomials
Step1: Multiply the coefficients.
Step2: Multiply powers with same base.
Step3: Simplify.
steps of multiplying monomials 2.0
Step0: Power of product.
Step1: Multiply the coefficients.
Step2: Multiply powers with same base. Step3: Simplify.
Multiplying a Monomial by a Polynomial
step2: Add all the products.
step1: Multiply all terms of the polynomial by the monomial. (Multiply coefficients and powers with the same base)
General Steps of Multiplying Polynomials
Step1: Multiply all terms of one polynomial by each term of the other polynomial.
Step2: Add all the products.
the square of the first, plus(or minus) twice the product of the first and second, plus the square of the second
(a+b)^2 = a^2 + 2ab +b^2
(a-b)^2 = a^2 - 2ab +b^2