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We Distribute, Yet Things Multiply · Class 8

5 questions · English, हिन्दी, मराठी · answer key with explanations ·

NCERT: Class 8 Ganita Prakash Part I, Chapter 6: We Distribute, Yet Things Multiply. Our own questions in the chapter's style, drafted with AI help, every answer checked step by step; teacher review pending. Hindi and Marathi: translation - review pending.

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We Distribute, Yet Things Multiply · English

Name: ____________________Date: ____________

Questions

  1. 23 × 101 = ?

  2. If a = 5 and b = 3, what is (a + b)²?

  3. Use (a + b)(a − b) = a² − b² to find 52 × 48.

  4. What is the value of (x + 3)(x + 4) when x = 2?

  5. Find 99 × 37 using 99 = 100 − 1.

Answer key

  1. 2323 — 23 × (100 + 1) = 2,300 + 23 = 2,323.
  2. 64 — (5 + 3)² = 8² = 64. Check with a² + 2ab + b² = 25 + 30 + 9 = 64.
  3. 2496 — 52 × 48 = (50 + 2)(50 − 2) = 2,500 − 4 = 2,496.
  4. 30 — (x + 3)(x + 4) = x² + 7x + 12 = 4 + 14 + 12 = 30. Check: 5 × 6 = 30.
  5. 3663 — 99 × 37 = 100 × 37 − 1 × 37 = 3,700 − 37 = 3,663.

हम बाँटते हैं, फिर भी चीज़ें गुणा होती हैं · हिन्दी

नाम: ____________________तारीख़: ____________

प्रश्न

  1. 23 × 101 = ?

  2. अगर a = 5 और b = 3 है, तो (a + b)² कितना है?

  3. (a + b)(a − b) = a² − b² से 52 × 48 ज्ञात करो।

  4. x = 2 होने पर (x + 3)(x + 4) का मान क्या है?

  5. 99 = 100 − 1 का उपयोग करके 99 × 37 ज्ञात करो।

उत्तर

  1. 2323 — 23 × (100 + 1) = 2,300 + 23 = 2,323।
  2. 64 — (5 + 3)² = 8² = 64। जाँच: a² + 2ab + b² = 25 + 30 + 9 = 64।
  3. 2496 — 52 × 48 = (50 + 2)(50 − 2) = 2,500 − 4 = 2,496।
  4. 30 — (x + 3)(x + 4) = x² + 7x + 12 = 4 + 14 + 12 = 30। जाँच: 5 × 6 = 30।
  5. 3663 — 99 × 37 = 100 × 37 − 1 × 37 = 3,700 − 37 = 3,663।

आपण वाटतो, तरी गोष्टी गुणल्या जातात · मराठी

नाव: ____________________दिनांक: ____________

प्रश्न

  1. 23 × 101 = ?

  2. जर a = 5 आणि b = 3 असेल, तर (a + b)² किती?

  3. (a + b)(a − b) = a² − b² वापरून 52 × 48 काढा.

  4. x = 2 असताना (x + 3)(x + 4) ची किंमत किती?

  5. 99 = 100 − 1 वापरून 99 × 37 काढा.

उत्तरे

  1. 2323 — 23 × (100 + 1) = 2,300 + 23 = 2,323.
  2. 64 — (5 + 3)² = 8² = 64. तपासा: a² + 2ab + b² = 25 + 30 + 9 = 64.
  3. 2496 — 52 × 48 = (50 + 2)(50 − 2) = 2,500 − 4 = 2,496.
  4. 30 — (x + 3)(x + 4) = x² + 7x + 12 = 4 + 14 + 12 = 30. तपासा: 5 × 6 = 30.
  5. 3663 — 99 × 37 = 100 × 37 − 1 × 37 = 3,700 − 37 = 3,663.

A worked example

Find 47 × 99 without long multiplication.

  1. 99 = 100 − 1, so 47 × 99 = 47 × 100 − 47 × 1.
  2. 4,700 − 47 = 4,653.

Answer: 4,653. Check: 47 × 99 = 99 × 47 = 99 × 40 + 99 × 7 = 3,960 + 693 = 4,653.

The common mistake

Multiplying only the first term in a bracket: 3(x + 4) written as 3x + 4. The 3 multiplies every term inside: 3x + 12.

In the NCERT book

Ganita Prakash Part I, Class 8 (Reprint 2026-27), Chapter 6: We Distribute, Yet Things Multiply, pages 136 to 170. Open the chapter (PDF).

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