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
$$(a + b)(a - b) = a^2 - b^2$$
See also
Discriminant of a quadratic polynomial