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Math Review Diagram 1.1-1.11 - Coggle Diagram
Math Review Diagram 1.1-1.11
Definition
What is Monomial（单项式）
Monomial is a product of a number and one or more variables with non-negative integer exponents. P.s. A single number or variable is also a monomial.
What is Polynomial （多项式）
Polynomial is a sum of monomials.
What is the value of Algebraic expression（代数式的值）
The value of Algebraic expressions is when a number represents each letter in the Algebraic formula, then the solution is the value of Algebraic expression.
What is like terms （同类项）
Like terms are terms with the same variable form.
What is a algebraic expression（代数式）
Algebraic expressions are formulas with letters and numbers connected together by calculation signs.
Calculation
Product of power with the same base
Keep the base and add exponents.
Power of product
e.g. (ab)^2=a^2b^2
Addition and Subtraction of monomials and polynomials
Step 1: Get rid of brackets.
Step 2: Combine like terms.
power of power
e.g. (a^2)^3=a^6
keep the base number and multiply exponents.
Multiplying monomials
Step 1: Multiply coefficient.
Step 2: Multiply powers with same base.
Step 3: Multiply other variables
Step 0: Calculate power of power or product.
Multiplying a monomial by a polynomial
Step 1: Multiply all terms of the polynomial by the monomial
Step 2: Simplify
Multiplying polynomials
Step 2: Add all products
Step 3: Combine all like terms and simplify.
Step 1: Multiply all terms of one polynomial with each term of the other polynomial.
Rule
When multiplying numbers with letters, place numbers at the front and ignore the multiplication sign.
When the coefficient is an mixed fraction, change it into an improper fraction.
Use fraction to represent division.
Formulas
Difference of squares formula
e.g. (a+b)(a-b)=a^2-b^2
The answer shapes as the square of the same term subtracting the square of the opposite terms.
How to show this formula?
(a+b)(a-b)=a^2-ab+ab-b^2=a^2-b^2
Using rectangles to show.
Perfect square formula
e.g. (a±b)^2=a^2±2ab+b^2
The answer shapes as the two terms' square add/subtracts (depending on the symbol of original expression) two times the product of the two terms
How to show formula?
(a+b)(a+b)=a^2+ab+ab+b^2=a^2+2ab+b^2
Use rectangles to show