We Distribute, Yet Things Multiply — Practice Quiz
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.
Show answer
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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