Special product formulas
Special products are algebraic formulas that allow you to quickly and directly calculate the result of certain multiplications of expressions, without having to apply term-by-term multiplication step by step.
Their importance lies in the fact that:
- They simplify calculations: they avoid long multiplications.
- They reveal recurring algebraic patterns found in many problems.
- They facilitate factorization and equation solving.
- They are essential tools in algebra and frequently appear in physics, engineering, and other sciences.
Table of special product formulas
| name | equation |
|---|---|
| square of a sum | $$(a + b)^2 = a^2 + 2ab + b^2$$ |
| Square of a difference | $$(a - b)^2 = a^2 - 2ab + b^2$$ |
| Difference of squares | $$(a + b)(a - b) = a^2 - b^2$$ |
| Cube of a sum | $$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$$ |
| Cube of a difference | $$(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$$ |
| Sum of cubes | $$(a + b)(a^2 - ab + b^2) = a^3 + b^3$$ |
| Difference of cubes | $$(a - b)(a^2 + ab + b^2) = a^3 - b^3$$ |
| Square of a trinomial | $$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$$ |
Interactive graphs
Square of a sum
$$(a + b)^2 = a^2 + 2ab + b^2$$
Square of a difference
$$(a - b)^2 = a^2 - 2ab + b^2$$
Difference of squares
Also known as product of a sum and a difference
$$(a + b)(a - b) = a^2 - b^2$$
Factorization
Factorization in algebra is the process of rewriting an expression as a product of simpler expressions whose multiplication reproduces the original expression. It is the reverse of expansion and is essential for solving equations, simplifying rational expressions, and analyzing functions.
Instructions
Write the results of the factorization between the parentheses and check the result.
See also
Discriminant of a quadratic polynomial