Binomial Formulas (Short Multiplication Formulas)
Interactive reference for all short multiplication formulas with step-by-step expansion calculator. Enter values for a and b to see results.
(a + b)² = a² + 2ab + b²= 25
(a − b)² = a² − 2ab + b²= 1
a² − b² = (a + b)(a − b)= 5
(a + b)³ = a³ + 3a²b + 3ab² + b³= 125
(a − b)³ = a³ − 3a²b + 3ab² − b³= 1
a³ + b³ = (a + b)(a² − ab + b²)= 35
a³ − b³ = (a − b)(a² + ab + b²)= 19
How to Use the Binomial Formulas (Short Multiplication Formulas)
- Browse the reference table to find the values you need.
- Use search or scroll to locate specific entries.
- Click on a value to copy it or see more details.
- Use the table as a quick reference during calculations or study.
Référence rapide
| De | Vers |
|---|---|
| 1 × 1 | 1 |
| 5 × 5 | 25 |
| 7 × 8 | 56 |
| 9 × 9 | 81 |
| 12 × 12 | 144 |
| 15 × 15 | 225 |
Cas d'utilisation
- •Quick lookup of values during math class or professional work.
- •Verifying calculations without needing a full scientific calculator.
- •Studying mathematical relationships, patterns, and properties.
- •Using as a handy reference during engineering or science tasks.
Formule
Short multiplication formulas (binomial identities) are algebraic identities that simplify the expansion of expressions involving sums, differences, and powers.
Questions fréquemment posées
What are short multiplication formulas?
Short multiplication formulas are algebraic identities such as (a+b)² = a² + 2ab + b² that allow you to quickly expand or factor polynomial expressions without performing full multiplication.
How do I use the difference of squares formula?
The formula a² − b² = (a+b)(a−b) lets you factor any difference of two squares. For example, 49 − 16 = 7² − 4² = (7+4)(7−4) = 11 × 3 = 33.
What is the sum of cubes formula?
a³ + b³ = (a+b)(a² − ab + b²). For example, 8 + 27 = 2³ + 3³ = (2+3)(4 − 6 + 9) = 5 × 7 = 35.
Why are these formulas important in algebra?
They are essential for simplifying expressions, solving equations, and factoring polynomials. They save time and reduce errors compared to expanding by brute force.