TLDR;
This video presents a mathematical trick to simplify multiplication of numbers that are equidistant from a central number. It uses the algebraic formula (a + b)(a - b) = a² - b² to quickly calculate the product of two numbers by squaring their average and subtracting the square of their difference from the average. The method is demonstrated with various examples, including multiplying numbers around 10, 20, and even larger numbers like 100 and 25.
- Utilizes the algebraic identity (a + b)(a - b) = a² - b² for quick multiplication.
- Focuses on finding the average (central number) between the two numbers being multiplied.
- Simplifies calculations by squaring the average and subtracting the square of the difference.
Introduction to the Multiplication Trick [0:58]
The video introduces a mathematical trick designed to simplify multiplication problems, particularly useful for competitive examinations. The core concept revolves around leveraging basic algebraic principles to expedite calculations. It focuses on multiplication, divisions, proportions, squares, square roots, cubes, cube roots, basic algebra equations, and geometry.
Understanding the Core Algebraic Formula [1:26]
The presenter explains the fundamental algebraic formula: (a + b) * (a - b) = a² - b². This formula is the foundation of the multiplication trick. Examples like (x + 1)(x - 1) = x² - 1² and (x + 2)(x - 2) = x² - 2² are used to illustrate the concept.
Applying the Formula with the Number 10 as the Base [3:40]
The presenter demonstrates the trick using 10 as the base number. For example, to multiply 12 by 8, the average number 10 is identified. The calculation becomes 10² - 2², which simplifies to 100 - 4 = 96. This method is applied to other examples like 11 * 9 and 13 * 7.
Extending the Trick to Numbers Around 20 [8:07]
The presenter extends the multiplication trick to numbers around 20. The key is to find the average number between the two numbers being multiplied and apply the same formula. For instance, to multiply 21 by 19, the average is 20. The calculation is 20² - 1² = 400 - 1 = 399.
Applying the Trick with Larger Numbers [11:29]
The presenter demonstrates the technique with larger numbers, such as those around 30. For example, to multiply 31 by 29, the average is 30. The calculation becomes 30² - 1² = 900 - 1 = 899. The method remains consistent, emphasizing the efficiency of this approach.
Multiplying Numbers Around 50 and 70 [14:49]
The presenter continues to illustrate the trick with numbers around 70. For example, to multiply 71 by 69, the average is 70. The calculation is 70² - 1² = 4900 - 1 = 4899. The presenter highlights the consistent application of the formula.
Applying the Trick with Numbers Around 100 [15:16]
The presenter explains how to use the trick with numbers around 100. For example, to multiply 102 by 98, the average is 100. The calculation is 100² - 2² = 10000 - 4 = 9996. This demonstrates the scalability of the trick to larger numbers.
Further Examples and Conclusion [19:31]
The presenter provides additional examples, such as multiplying 24 by 26, where the average is 25. The calculation is 25² - 1² = 625 - 1 = 624. The video concludes by encouraging viewers to utilize this method for quick calculations in various competitive exams and civil services.