HOW TO SOLVE THIS MATHS PROBLEM WITHOUT A CALCULATOR..FASTAND STEP BY STEP EXPLANATION#mathsproblem

SS Online Tutor
2 Sept 202405:19

TLDRIn this educational video, the host demonstrates how to solve a complex math problem without a calculator. By assigning the value of 20 to x, the problem simplifies to expressions involving x, x-1, x+1, x-2, and x+2. Using the formula for the square of a difference, the host then multiplies terms to form a polynomial, which is solved by substituting x with 20. The final step involves multiplying 20 by a series of numbers to reach the solution for the product of 18, 19, 20, 21, and 22. The host encourages viewers to follow along and practice this method for solving similar problems.

Takeaways

  • 🧮 Solve math problems without a calculator by substituting variables for numbers.
  • 🔢 Assume 'x' equals 20 and replace other numbers in the problem with expressions involving 'x'.
  • ➖ Convert the problem into algebraic expressions using 'x', such as 'x - 2' for 18, 'x + 2' for 22, etc.
  • 🔄 Use the identity (a - b)(a + b) = a² - b² to simplify the expressions.
  • 📚 Recognize that x(x² - 1) can be rewritten as x³ - x using the distributive property.
  • 🔢 Expand the expressions to get x⁴ - 5x² + 4 by multiplying (x²)(x² - 4).
  • 📈 Substitute the value of x (20) into the expanded expression to calculate the result.
  • 🧮 Calculate 20⁴ as 160000 by multiplying 20 by itself four times.
  • ➖ Subtract 5 times 20² (which is 20 * 20) and add 4 to get the final result.
  • 📝 The final answer to the problem involving the product of numbers 18, 19, 20, 21, and 22 is obtained by following these steps.

Q & A

  • What is the main objective of the video?

    -The main objective of the video is to solve a math problem step by step without using a calculator.

  • Why does the presenter assume the value of x to be 20?

    -The presenter assumes the value of x to be 20 to simplify the problem and to demonstrate how to solve it without a calculator by substituting the given numbers with expressions involving x.

  • What is the significance of substituting 18, 19, 20, 21, and 22 with expressions involving x?

    -Substituting the numbers with expressions involving x allows the presenter to use algebraic identities and simplifications to solve the problem more easily.

  • What algebraic identity is used in the video to simplify the expression (x - 1)(x + 1)?

    -The algebraic identity used is the difference of squares, which states that (a - b)(a + b) = a² - b².

  • How does the presenter expand the expression (x² - 1)(x² - 4)?

    -The presenter expands the expression by multiplying x² with x² to get x⁴ and then subtracting the product of the constants -1 * -4 to get +4, resulting in x⁴ - 5x² + 4.

  • What is the final expression obtained after substituting x with 20 in the expanded expression?

    -The final expression after substituting x with 20 is 20⁴ - 5*20² + 4.

  • How does the presenter calculate 20⁴?

    -The presenter calculates 20⁴ by multiplying 20 by itself four times, which results in 160000.

  • What is the final answer to the problem after performing all the calculations?

    -The final answer to the problem is 1584000, which is the product of 18, 19, 20, 21, and 22.

  • Why does the presenter multiply 20 by 10 and then by 2 in the calculation?

    -The presenter multiplies 20 by 10 and then by 2 to simplify the calculation of 20², which is a part of the process to find 20⁴.

  • What is the educational value of the video for viewers?

    -The video provides an educational value by demonstrating how to solve complex multiplication problems using algebraic identities and step-by-step calculations without a calculator.

Outlines

00:00

🧮 Solving a Mathematical Problem Without a Calculator

This paragraph introduces a mathematical problem that needs to be solved without using a calculator. The presenter begins by assigning the value of 20 to the variable x and then substitutes values like 18 as x-2, 19 as x-1, and so on, in an equation. The presenter uses the formula (x - 1)(x + 1) which simplifies to x^2 - 1, and then expands it to x^4 - 4x^2. The goal is to calculate the product of the numbers 18, 19, 20, 21, and 22 by substituting x with 20 and performing the calculation step by step. The presenter demonstrates the process of multiplying 20 by itself multiple times and then subtracting and adding the results to reach the final answer. The explanation is methodical, focusing on the algebraic manipulation and arithmetic involved in the calculation.

05:03

📢 Conclusion and Channel Promotion

In this concluding paragraph, the presenter summarizes the solution to the mathematical problem and provides the final answer. They also invite viewers who are new to the channel to subscribe, like, and share the video. This is a common practice in educational content creation to engage the audience and grow the channel's following. The presenter emphasizes the importance of understanding the process and encourages viewers to practice similar problems to improve their mathematical skills.

Mindmap

Keywords

💡Calculator

A calculator is an electronic device used to perform mathematical operations. In the context of the video, the challenge is to solve the math problem without using a calculator, emphasizing the importance of understanding mathematical concepts and being able to perform calculations mentally or manually.

💡Assume

To assume means to suppose or take for granted without proof. In the video, the presenter starts by assuming the value of 'x' to be 20, which is a common technique in problem-solving to simplify the equation or expression by substituting a variable with a chosen value.

💡Value of x

The 'value of x' refers to the numerical substitution made for the variable 'x' in an equation or expression. The video uses the value 20 for 'x' to demonstrate how to solve the problem step by step, making it easier to visualize and calculate the subsequent steps.

💡Formula

A formula in mathematics is a set of symbols representing a rule or a relationship between quantities. The script mentions the formula 'x - 1' and 'x + 1', which are used to express the numbers 19 and 21 in relation to the assumed value of 'x'. This helps in applying algebraic identities to simplify the problem.

💡Algebraic identity

An algebraic identity is an equality that holds true for all values of the variables involved. The video references the identity (a - b)(a + b) = a² - b², which is used to transform the product of 'x - 1' and 'x + 1' into a more manageable form, x² - 1.

💡Exponentiation

Exponentiation is the operation of raising a number to the power of another number. In the video, the presenter calculates 20 to the power of 4, which is a key step in finding the product of the series 18 * 19 * 20 * 21 * 22 without a calculator.

💡Multiplication

Multiplication is a mathematical operation where one number is added to itself a specified number of times. The video demonstrates the process of multiplying large numbers, such as 20 * 20, which is part of the calculation to solve the problem.

💡Subtraction

Subtraction is the mathematical operation of removing one quantity from another. The video script shows the subtraction of large numbers, such as when calculating 20^4 - 5 * 20^2 + 4, which is part of the process to find the final answer.

💡Series

A series in mathematics is the sum of the terms of a sequence. The problem presented in the video involves calculating the product of a series of consecutive numbers, specifically 18 to 22, which is a type of series known as an arithmetic sequence.

💡Mental Math

Mental math refers to the ability to perform arithmetic operations in one's mind without the use of external tools like a calculator. The video's main theme is to demonstrate how to solve a complex multiplication problem using mental math techniques, showcasing strategies for simplifying and calculating large numbers.

Highlights

Introduction to solving a math problem without a calculator.

Assumption of the value of x as 20 for simplification.

Substitution of numbers with expressions involving x: 18 as x - 2, 19 as x - 1, 20 as x, 21 as x + 1, and 22 as x + 2.

Explanation of the formula x - 1 and x + 1 as a difference of squares.

Application of the identity (a - b)(a + b) = a² - b².

Multiplication of terms to form x⁴ - 4x².

Further simplification to x⁴ - 5x² + 4.

Substitution of x with 20 to calculate 20⁴ - 5*20² + 4.

Step-by-step calculation of 20⁴ as 160000.

Calculation of -5*20² as -20000.

Final calculation resulting in 1584000.

Breaking down 20 into 10 and 2 for further multiplication.

Multiplication of 10*20 and 2*20 to get the final product.

Final answer calculation for the product of 18, 19, 20, 21, and 22.

Encouragement for new viewers to subscribe, like, and share the channel.