Mathematics lesson

0. Monomials, polynomials and operations with them

1. Formulas for abbreviated multiplication. Formula for the square of a binomial - $(a\pm b)^2=a^2\pm 2ab+b^2$

2. Formula for the product of a sum by a difference of a binomial - $(a-b)(a+b)=a^2-b^2$

3. Formulas for abbreviated multiplication. Formula for the cube of a binomial - $(a\pm b)^3=a^3\pm 3a^2b+3ab^2\pm b^3$

4. Formula for the sum and difference of the cubes of two numbers - $(a\pm b)(a^2\mp ab+b^2)$

5. Common problems from the short multiplication formulas

6. Decomposing a polynomial into factors by applying the formulas for short multiplication