Basic maths

 Solve the following 

1. (a+b)² = __________

2. (a-b)² = ___________

3. (a+b)³ = __________

4. (a-b)³ = ___________

5. (a+b)² - 2ab = ___________

6. (a+b)² + ( a-b)² = ___________

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NATIONAL MATHEMATICS DAY

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  Srinivasa Ramanujan – The Man Who Knew Infinity Introduction Srinivasa Ramanujan was one of the greatest mathematicians the world has ever known. He was not just a mathematician, but a symbol of pure genius, dedication, and faith. Born in poverty, without formal higher education in mathematics, Ramanujan made discoveries that still influence modern mathematics today. His life story is both inspiring and heartbreaking, showing how talent can rise even in the hardest conditions. Early Life and Family Background Srinivasa Ramanujan was born on 22 December 1887 in Erode, a small town in the Madras Presidency (now Tamil Nadu, India). His father, Kuppuswamy Srinivasa Iyengar, worked as a clerk in a cloth merchant’s shop, earning a very modest income. His mother, Komalatammal, was a housewife and a devout religious woman who sang devotional songs at a local temple. Ramanujan grew up in Kumbakonam, where the family faced financial difficulties throughout his childhood. From a very young ...
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How to Find the Value of ab When a+b and a²+b² Are Given

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 Here’s a Blogger-ready post with title, content, and clear answer 👇 Title: How to Find the Value of ab When a+b and a²+b² Are Given Content is In algebra, many problems can be solved easily by using identities instead of lengthy calculations. Let us see one such example. Given: a^2 + b^2 = 100 and a+b=12 We are asked to find the value of ab. Step 1: Use the identity    (a+b)² = a² + b² + 2ab => (a+b)²  - 2ab = a² + b² Step 2: Substitute the given values    100 = (12)² -2ab => 100 = 144 - 2ab Step 3: Solve for ab     2ab = 144 - 100 => 2ab = 44 => ab = 22 Final Answer:  ab = 22 Conclusion: Using algebraic identities helps us solve problems quickly and accurately. This method is very useful in exams and competitive tests.
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  Easy Trick to Subtract 9 (e.g., 18 − 9) Trick idea: Instead of subtracting 9 directly, make it easier by using 10. Add 1 to the number you’re subtracting from (the minuend). → 18 + 1 = 19 Now subtract 9 from 19. → 19 − 9 = 10 Subtract the 1 you added earlier. → 10 − 1 = 9 ✔ So 18 − 9 = 9 using this trick! This works because 9 = 10 − 1, so adding 1 and later removing it makes mental subtraction easier. � 📌 Why It Works (Simple Explanation) When you want to subtract 9, think of 9 as (10 − 1): Instead of directly subtracting 9, subtract 10 (easy!) Then add back 1 (because you subtracted one too many) ➡ That’s exactly what your steps do: Add 1 → subtract 9 Equivalent to subtracting 10 then adding 1. � Jagranjosh.com ✍️ Example way :-  Here’s a ready-to-paste explanation you can use: Super Fast Trick to Subtract 9! To solve 18 − 9 quickly in your mind: 1️⃣ Add 1 to 18 → 19 2️⃣ Subtract 9 → 10 3️⃣ Subtract 1 → 9 So, 18 − 9 = 9 🧠💡 (Why? Because 9 is just 10 − 1, so adding and re...
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