We Distribute, Yet Things Multiply — Quiz

Q1. Ravi observes that 23 × 27 = 621. He then increases both numbers by 1 and computes 24 × 28. Using distributivity, by how much does the product increase?

• A. 1
• B. 23
• C. 51
• D. 50

Q2. Priya computes 24 × 26 after taking 25 × 25. Using (a + 1)(b − 1) = ab + b − a − 1, what happens to the product compared with 25 × 25?

• A. Increases by 1
• B. Decreases by 25
• C. Stays the same
• D. Decreases by 1

Q3. A student writes (a + b) × c = c × (a + b) = ca + cb. Which two properties has she used, in order?

• A. Distributivity, then commutativity
• B. Distributivity twice
• C. Associativity, then commutativity
• D. Commutativity, then distributivity

Q4. Manju expands (10a + b)(10c + d) using Identity 1. Which expression does she correctly obtain?

• A. 10ac + bd
• B. 10ac + ad + bc + bd
• C. 100ac + bd
• D. 100ac + 10ad + 10bc + bd

Q5. Tenzin uses Identity 1 to expand (−5a + b)(c + d). What does he get?

• A. −5ac − 5ad + bc + bd
• B. −5ac + bd
• C. 5ac + 5ad + bc + bd
• D. −5ac − 5ad − bc − bd

Q6. If a is increased by m and b by n, by how much does the product ab change?

• A. mn
• B. am + bn
• C. a + b + mn
• D. an + bm + mn

Q7. Expands (6x + 5)^2 using Identity 1A. Which expression is the correct expansion?

• A. 36x^2 + 25
• B. 36x^2 + 30x + 25
• C. 12x^2 + 60x + 25
• D. 36x^2 + 60x + 25

Q8. Aarti writes 104 = 100 + 4 and uses Identity 1A to find 104^2. What value does she get?

• A. 10816
• B. 10016
• C. 10800
• D. 10416

Q9. On students are asked to find 99^2 using Identity 1B with a = 100 and b = 1. What value do they get?

• A. 9801
• B. 9999
• C. 9800
• D. 10001

Q10. Using Identity 1B, the expansion of (b − 6)^2 is

• A. b^2 − 36
• B. b^2 + 12b + 36
• C. b^2 − 12b + 36
• D. b^2 − 6b + 36

Q11. Yusuf is asked to compute 45 × 55 using Identity 1C. Writing 45 = 50 − 5 and 55 = 50 + 5, what value does he get?

• A. 2475
• B. 2500
• C. 2525
• D. 2575

Q12. Which mathematician (around 750 CE) gave a fast-squaring method based on Identity 1C, using the form a^2 = (a + b)(a − b) + b^2?

• A. Aryabhata
• B. Brahmagupta
• C. Sridharacharya
• D. Bhaskaracharya

Q13. Using Sridharacharya's method 31^2 is written as (31 + 1)(31 − 1) + 1^2. What value does this give?

• A. 960
• B. 931
• C. 962
• D. 961

Q14. In 'Mind the Mistake' Q8 a student writes 5w^2 + 6w = 11w^2. What is the error?

• A. 5w^2 and 6w are not like terms — they cannot be combined
• B. She should have written 11w^3
• C. She should have written 30w^3
• D. The expression is already in simplest form 5w^2 + 6w

Q15. Derives a one-line rule for a 4-digit number dcba × 101 using dcba × (100 + 1). Which expression equals dcba × 101?

• A. dcba + 101
• B. 100 × 101 × dcba
• C. dcba × 100 + 1
• D. dcba × 100 + dcba