Rucete ✏ Mathematics In a Nutshell
Expansion | In a nutshell
The term "expand" refers to the process of multiplying in order to remove the ( ).
Example
2(2x + 1) = 4x +2
In general, to remove (), we proceed with the addition, subtraction, multiplication, and division according to the situation, but memorizing a few rules can speed up the calculation process.
Rule
1. (a + b)² = a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
3. (a + b)(a - b) = a² - b²
4. (x + a)(x - b) = x² + (a + b)x + ab
5. (ax + b)(cx + d) = acx² + (ad + bc)x + bd
6. (a ± b)³ = a³ ± 3a²b + 3ab² ± b³
7. (a + b)(a² - ab + b²) = a³ + b³
8. (a - b)(a² + ab + b²) = a³ - b³
9. (a + b + c)(a² + b² + c² - ab - bc - ca) or 1/2(a + b + c){(a - b)² + (b - c)² + (c - a)²} = a³ + b³ + c³ - 3abc
Example
1. (2x + 3)² = 4x² + 12x + 9
2. (2x - 3y)(2x+3y) = 4x² - 9y²
3. (sin x - 3)(sin x + 4) = sin² x + sin x - 12