We Distribute, Yet Things Multiply
CBSE · Class 8 · Mathematics
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Quick Quiz: We Distribute, Yet Things Multiply
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Hard calculation: Expand (a + u)(b - v) using the distributive property and identify the correct simplified form.
Hard calculation: Expand (a - u)(b + v) and choose the correct expression.
Hard calculation: Expand (a - u)(b - v) using the distributive property.
Hard calculation: Find the expansion of (a + b) × (a^2 + 2ab + b^2).
Sample Questions
Hard calculation: A number 3874 is multiplied by 11. What product is obtained using distributive property?
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42614
Use 3874 × 11 = 3874(10 + 1) = 38740 + 3874 = 42614. The tens-place shift and addition give the final product.
Hard calculation: A 4-digit number dcba is multiplied by 11. Which digit pattern appears in the result?
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d, c+d, b+c, a+b, a
Multiplying by 11 is the same as multiplying by 10 and adding the original number. Each middle digit is formed by adding adjacent digits, so the pattern is d, c+d, b+c, a+b, a.
Hard calculation: If the number of circles at Step k is k^2 + 2k, how many circles are there at Step 12?
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168
Substitute k = 12: k^2 + 2k = 12^2 + 2(12) = 144 + 24 = 168. The final answer is 168 circles.
Hard calculation: Using the formula a(b + 1) = ab + a, find the increase in product when 48 is multiplied by 19 instead of 18.
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48
The second factor increases by 1, so the product increases by the first factor. Here the first factor is 48, so the increase is 48.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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