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 teaches viewers how to solve a complex math problem without a calculator. By assigning the value of 20 to x and simplifying the problem step by step, the host demonstrates the use of algebraic identities like (a - b)(a + b) = a² - b². The solution involves expanding expressions and multiplying powers of 20, ultimately leading to the final answer for the product of 18, 19, 20, 21, and 22. The host encourages engagement by inviting viewers to subscribe, like, and share the video.

Takeaways

  • 🔢 To solve the math problem without a calculator, assign the value of x as 20.
  • 📝 Substitute the given numbers with expressions in terms of x: 18 as x - 2, 19 as x - 1, 20 as x, 21 as x + 1, and 22 as x + 2.
  • 🔄 Recognize the pattern in the problem as a difference of squares formula (a² - b²).
  • 📐 Use the formula x² - 1 = (x - 1)(x + 1) and x² - 4 = (x - 2)(x + 2) to simplify the expressions.
  • 💡 Multiply the simplified terms to get x⁴ - 5x² + 4.
  • 🔢 Replace x with 20 and calculate 20⁴ - 5*20² + 4.
  • 🧮 Perform the multiplication and addition step by step to get the final numerical result.
  • 📉 Subtract the terms to get the intermediate result of 15840.
  • 📈 Multiply 20 by the intermediate result to get the final answer.
  • 🎓 The final answer for the product of 18, 19, 20, 21, and 22 is obtained by following these steps.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is solving a math problem without a calculator, specifically involving the multiplication of consecutive numbers 18, 19, 20, 21, and 22.

  • How does the video suggest to approach the problem?

    -The video suggests to approach the problem by substituting the value of x with 20 and then expressing the other numbers in terms of x (e.g., 18 as x - 2, 19 as x - 1, etc.).

  • What is the formula used to simplify the expression x - 1 and x + 1?

    -The formula used to simplify the expression (x - 1)(x + 1) is the difference of squares, which is a^2 - b^2 where a = x and b = 1.

  • How does the video demonstrate the multiplication of (x - 1)(x + 1)?

    -The video demonstrates the multiplication by expressing it as x^2 - 1, which is derived from the difference of squares formula.

  • What is the next step after simplifying (x - 1)(x + 1)?

    -The next step is to multiply this result by another similar expression, (x - 2)(x + 2), which is also a difference of squares, resulting in x^4 - 4x^2.

  • How is the expression x^4 - 5x^2 + 4 simplified in the video?

    -The expression is simplified by substituting the value of x with 20, and then performing the multiplication and addition of the resulting terms.

  • What is the final calculation shown in the video for 20^4 - 5*20^2 + 4?

    -The final calculation shown is 20^4 - 5*20^2 + 4, which involves calculating 20 raised to the power of 4, multiplying 5 by 20 squared, and then adding 4.

  • How does the video handle the large number calculations?

    -The video handles large number calculations by breaking down the numbers into smaller parts, multiplying them step by step, and then combining the results.

  • What is the final answer to the multiplication problem as presented in the video?

    -The final answer to the multiplication problem of 18 * 19 * 20 * 21 * 22 is presented as a large number, which is calculated by following the steps shown in the video.

  • What is the advice given to new viewers of the channel at the end of the video?

    -The advice given to new viewers is to subscribe to the channel, like, and share the videos.

Outlines

00:00

🔢 Solving a Math Problem Without a Calculator

The speaker begins by welcoming viewers to their channel and introducing a math problem that needs to be solved without a calculator. They suggest assuming the value of x to be 20 and substituting values accordingly. The speaker then demonstrates how to use algebraic identities to simplify the problem, specifically using the formula (a - b)(a + b) = a² - b². They proceed to multiply terms involving x² and simplify the expression to x⁴ - 5x² + 4. The speaker then replaces x with 20 and calculates 20⁴ - 5*20² + 4, showing the step-by-step calculation process. They conclude by multiplying 20 by 10 and 20 by 2 to get the final answer for the product of 18, 19, 20, 21, and 22.

05:03

📢 Closing Remarks and Call to Action

In the concluding paragraph, the speaker summarizes the solution to the math problem and invites viewers to subscribe to their channel, like, and share their videos. This serves as a call to action for new viewers to engage with the content and join the community.

Mindmap

Keywords

💡Calculator

A calculator is an electronic device used to perform calculations, both basic and complex. In the context of the video, the challenge is to solve a math problem without using a calculator, emphasizing mental math and algebraic manipulation skills. The video aims to teach viewers how to handle mathematical operations manually, which is an essential skill for quick problem-solving.

💡Assume

To assume in mathematics often means to take a value as a starting point for further calculations or proofs. In the video, the presenter assumes the value of 'x' to be 20 to simplify the problem. This is a common technique in algebra to make equations more manageable and to illustrate the process of solving equations without a calculator.

💡Value of x

In algebra, 'x' typically represents an unknown value that we are trying to find. In the video, 'x' is assigned the value of 20 to replace other numbers in the problem, making it easier to apply algebraic formulas and perform calculations. This substitution is a strategic move to demonstrate how to handle complex expressions without a calculator.

💡Formula

A formula in mathematics is a relationship expressed in symbols, often involving operations among quantities. The video references the formula \( (a - b)(a + b) = a^2 - b^2 \), which is a difference of squares. This formula is used to simplify the multiplication of two binomials, showcasing an efficient method for solving the problem at hand without a calculator.

💡Simplify

Simplification in mathematics involves reducing a complex expression to a simpler form. The video demonstrates how to simplify the given problem by substituting 'x' with 20 and then applying algebraic identities. This process is crucial for making calculations more straightforward and for understanding the underlying structure of mathematical expressions.

💡Algebraic manipulation

Algebraic manipulation refers to the process of transforming algebraic expressions using various mathematical rules and identities. The video uses this technique to solve the problem without a calculator, showing how to multiply and combine terms to reach the solution. This skill is vital for performing mental calculations and for understanding the properties of numbers and operations.

💡Exponentiation

Exponentiation is the operation of raising a number to a power. In the video, the presenter calculates \( 20^4 \) as part of the problem-solving process. Understanding exponents is essential for handling large numbers and performing operations that would be cumbersome with basic multiplication and addition.

💡Substitution

Substitution is the process of replacing a variable or an expression with a specific value or another expression. The video uses substitution by assigning values to 'x' and other variables to simplify the problem. This method is a fundamental algebraic technique that helps in solving equations and performing calculations without a calculator.

💡Multiplication

Multiplication is one of the four basic arithmetic operations, involving the addition of a number by itself a certain number of times. In the video, the presenter multiplies large numbers to solve the problem, demonstrating the process without a calculator. This operation is fundamental in mathematics and is often used in complex calculations.

💡Mental Math

Mental math refers to the ability to perform arithmetic operations in one's head without using external tools like a calculator or paper. The video's main theme revolves around solving a math problem using mental math, which is a valuable skill for quick calculations and enhancing mathematical intuition.

💡Arithmetic Series

An arithmetic series is a sequence of numbers with a common difference between consecutive terms. In the video, the numbers 18, 19, 20, 21, and 22 form such a series. The presenter uses this series to demonstrate how to multiply a sequence of numbers without a calculator, which is a practical application of series in mathematics.

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.

Use of algebraic identities to simplify expressions.

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

Multiplication of terms to form a polynomial.

Substitution of the value of x (20) into the polynomial.

Calculation of 20 to the power of 4.

Explanation of the process to multiply large numbers.

Subtraction of terms to simplify the expression.

Final multiplication to find the product of the sequence.

Presentation of the final answer.

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

Emphasis on understanding the step-by-step process.

Highlighting the importance of algebraic manipulation in problem-solving.

Demonstration of mental math techniques for complex calculations.

Explanation of carrying over in multiplication.

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