Factorisation Ex 14.4 Class 8 NCERT: Finding and Correcting Errors

Welcome! In this chapter on Factorisation, Exercise 14.4 is a bit different and very important. It's like being a math detective! Instead of just solving problems, you'll be given mathematical statements that have errors in them. Your mission is to find these mistakes and correct them. This exercise is designed to make your algebra skills super strong by teaching you to be careful and precise.

Why is this important? Catching errors is a key skill in maths and in life. This exercise will train your brain to spot common algebraic mistakes, especially with brackets, squares, and substitution. By the end of this lesson, you will master the technique of comparing the Left Hand Side (LHS) and Right Hand Side (RHS) of an equation to verify its accuracy and provide the correct mathematical statement. Let's get started and become expert error-finders!

The Art of Error Detection in Algebra

In algebra, we often work with statements that claim two expressions are equal, like 4(x - 5) = 4x - 20. This is a correct statement. But what if you saw 4(x - 5) = 4x - 5? It looks similar, but is it correct? Exercise 14.4 is all about tackling such questions. The main task is to check if a given mathematical statement (an equation) is true or false. If it's false, you must identify the error and write the correct statement.

The most reliable method is to work with the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation. Pick one side, usually the one that looks more complicated (like the one with brackets), and simplify it using the rules of algebra you've learned. Once you can't simplify it any further, compare your result with the other side of the original equation. If they match, the statement is correct. If they don't, you've found the error! Your simplified expression is the correct version.

How to Find and Correct Errors: A Step-by-Step Guide

  1. Step 1: Identify LHS and RHS — Look at the given mathematical statement. The expression on the left of the equals sign (=) is the Left Hand Side (LHS). The expression on the right is the Right Hand Side (RHS).
  2. Step 2: Simplify the LHS — Take the LHS expression and simplify it completely. Use the distributive property for brackets, algebraic identities for squares, or combine like terms as needed. Do not look at the RHS while doing this.
  3. Step 3: Compare Your Result with the RHS — Now, compare the simplified expression you got in Step 2 with the original RHS given in the question. Are they the same?
  4. Step 4: Pinpoint the Error and Correct It — If your simplified LHS is different from the given RHS, the original statement is incorrect. The error is the difference between the two. The correct statement is: LHS = Your Simplified Result.

Worked Example: Finding an Error

  • Question: Find and correct the error in the mathematical statement: (2x)² + 5x = 4x + 5x Solution: Step 1: Identify LHS and RHS. LHS = (2x)² + 5x RHS = 4x + 5x Step 2: Simplify the LHS. Let's simplify the LHS: (2x)² + 5x Remember, (2x)² means (2x) * (2x), which is 4x². So, the LHS simplifies to 4x² + 5x. Step 3: Compare with the RHS. Our simplified LHS is 4x² + 5x. The given RHS is 4x + 5x (which simplifies to 9x). Clearly, 4x² + 5x is NOT equal to 9x. Step 4: Correct the Statement. The error is that (2x)² was incorrectly written as 4x instead of 4x². The correct statement is: (2x)² + 5x = 4x² + 5x.

Common Mistakes to Watch Out For

When working on Factorisation Ex 14.4, be on the lookout for these very common errors. Teachers often use them in questions!

  • Incorrect Distributive Property: Forgetting to multiply the second term in a bracket. Wrong: 3(x + 4) = 3x + 4. Correct: 3(x + 4) = 3x + 12.
  • Incorrect Squaring of a Binomial: Applying the square to each term individually. Wrong: (x + 5)² = x² + 25. Correct: (x + 5)² = x² + 10x + 25 using (a+b)² = a² + 2ab + b².
  • Incorrect Cancellation in Fractions: Cancelling terms that are added or subtracted. Wrong: (3x + 2) / 3x = 1 + 2. Correct: You cannot cancel the 3x terms like this. The expression cannot be simplified by cancellation.
  • Substituting a Value Incorrectly: When you replace x with a negative number, like -3, be careful. x² becomes (-3)² = 9, not -9.

Practice Questions with Solutions

  • Q: Find and correct the error in the statement: 5y + 2y + y - 7y = 0 A: Step 1: Identify the LHS: 5y + 2y + y - 7y. Step 2: Simplify the LHS by combining like terms. 5y + 2y + y = 8y. So the expression becomes 8y - 7y, which is y. Step 3: Compare the simplified LHS (y) with the given RHS (0). They are not equal. Final answer: The error is that the sum was assumed to be 0. The correct statement is 5y + 2y + y - 7y = y.
  • Q: Find and correct the error in the statement: (z + 5)² = z² + 25 A: Step 1: Identify the LHS: (z + 5)². Step 2: Simplify the LHS using the identity (a+b)² = a² + 2ab + b². Here, a=z and b=5. So, (z + 5)² = z² + 2(z)(5) + 5² = z² + 10z + 25. Step 3: Compare the simplified LHS (z² + 10z + 25) with the given RHS (z² + 25). The term 10z is missing. Final answer: The error is the omission of the middle term 2ab. The correct statement is (z + 5)² = z² + 10z + 25.
  • Q: Find and correct the error in the statement: Substituting x = -3 in x² + 5x + 4 gives (-3)² + 5(-3) + 4 = 9 + 15 + 4 = 28. A: Step 1: Let's re-do the substitution in the expression x² + 5x + 4 with x = -3. Step 2: The substitution is (-3)² + 5(-3) + 4. (-3)² is 9. 5(-3) is -15. So the expression is 9 - 15 + 4. Step 3: Calculate the result: 9 - 15 is -6. And -6 + 4 is -2. The given result is 28. Final answer: The error was in multiplying 5(-3) as +15 instead of -15. The correct result is (-3)² + 5(-3) + 4 = 9 - 15 + 4 = -2.
  • Q: Find and correct the error in the statement: (4x+5) / 4x = 5 A: Step 1: Identify the LHS: (4x+5) / 4x. Step 2: To simplify this fraction, we must divide each term in the numerator by the denominator: (4x/4x) + (5/4x). Step 3: 4x/4x = 1. So the expression simplifies to 1 + 5/(4x). This cannot be simplified further. Step 4: Compare the simplified LHS (1 + 5/(4x)) with the given RHS (5). They are not equal. Final answer: The error is improper cancellation. You cannot cancel only one part of a sum in the numerator. The correct statement is (4x+5) / 4x = 1 + 5/(4x).

Frequently Asked Questions

What is the main goal of Factorisation Exercise 14.4?

The main goal is to build accuracy in algebra. It teaches you to carefully check your work by spotting and correcting common errors in mathematical statements.

What are LHS and RHS, and why are they important here?

LHS stands for Left Hand Side and RHS for Right Hand Side of an equation. We simplify the LHS and compare it to the RHS to check if the statement is true, which is the core method for this exercise.

Can I simplify the RHS instead of the LHS?

Yes, absolutely! You should always simplify the side that is more complex. While it's usually the LHS, if the RHS has brackets or needs simplification, you can start there.

Is (x-5)² the same as x² - 25?

No, this is a very common mistake. You must use the identity (a-b)² = a² - 2ab + b². So, (x-5)² = x² - 10x + 25.