Квадрат суммы и квадрат разности
Squaring a Sum and Squaring a Difference
Формулы сокращённого умножения — Short Multiplication Formulas
Алгебра · 7 класс1. Введение — Introduction
In algebra, we often need to square expressions like (a + b)² or (a − b)². These are two of the most important формулы сокращённого умножения (short multiplication formulas).
Why learn these formulas?
- Squaring a binomial is one of the most common operations in algebra
- The formulas make calculations fast and accurate
- They help you factor expressions and simplify equations
- You will use them in every math course from now on!
2. Deriving the Square of a Sum — Вывод формулы квадрата суммы
Let's derive the formula step by step. We start with the definition of squaring:
(a + b)² = (a + b)(a + b)
Now multiply as polynomials — each term in the first bracket by each term in the second:
| × | a | +b |
|---|---|---|
| a | a² | +ab |
| +b | +ab | +b² |
= a² + ab + ab + b²
= a² + 2ab + b²
The two middle terms ab + ab combine to give 2ab