# NCERT Class 8 Mathematics Chapter 6 We Distribute, yet Things Multiply Solutions: In-Text and Exercise Questions Explained | SwaVid

Here are the questions and step-by-step solutions from NCERT Class 8 Mathematics textbook "Ganita Prakash", Chapter 6: "We Distribute, yet Things Multip...

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# We Distribute, yet Things Multiply

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Chapter 6 · Class 8 Mathematics

Here are the questions and step-by-step solutions from NCERT Class 8 Mathematics textbook "Ganita Prakash", Chapter 6: "We Distribute, yet Things Multiply".

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In-text Questions (Page 136-137)

Answer: 1. The product increases by 27.
2. The product increases by 23.
3. The product increases by 51.
General Pattern: If two numbers 'a' and 'b' are increased by 'm' and 'n' respectively, the product increases by an + bm + mn.

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- Original product: 23 × 27 = 621.
- Part 1: First number (23) increased by 1. New numbers are (23 + 1) and 27, which is 24 × 27.
- Using distributive property: (23 + 1) × 27 = 23 × 27 + 1 × 27 = 621 + 27 = 648.
- Increase in product = 648 - 621 = 27.
- Part 2: Second number (27) increased by 1. New numbers are 23 and (27 + 1), which is 23 × 28.
- Using distributive property: 23 × (27 + 1) = 23 × 27 + 23 × 1 = 621 + 23 = 644.
- Increase in product = 644 - 621 = 23.
- Part 3: Both numbers increased by 1. New numbers are (23 + 1) and (27 + 1), which is 24 × 28.
- Using distributive property: (23 + 1) × (27 + 1) = 23 × 27 + 23 × 1 + 1 × 27 + 1 × 1 = 621 + 23 + 27 + 1 = 672.
- Increase in product = 672 - 621 = 51.
- General Pattern: If two numbers 'a' and 'b' are multiplied, and 'a' is increased by 'm' and 'b' is increased by 'n', the new product is (a + m)(b + n).
- Expanding this: (a + m)(b + n) = ab + an + bm + mn.
- The original product is ab. The increase in the product is (ab + an + bm + mn) - ab = an + bm + mn.
- For Part 1 (a=23, b=27, m=1, n=0): Increase = 23(0) + 27(1) + 1(0) = 27.
- For Part 2 (a=23, b=27, m=0, n=1): Increase = 23(1) + 27(0) + 0(1) = 23.
- For Part 3 (a=23, b=27, m=1, n=1): Increase = 23(1) + 27(1) + 1(1) = 23 + 27 + 1 = 51.
- NCERT Class 8 Mathematics textbook: Ganita Prakash : Chapter 6: We Distribute, yet Things Multiply

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