We Distribute, Yet Things Multiply — Practice

Q1. Which equation states the distributive property of multiplication over addition for any three numbers a, b and c?

• A. a + (b × c) = (a + b) × (a + c)
• B. a × (b × c) = (a × b) × c
• C. a × (b + c) = a × b + a × c
• D. a × b = b × a

Q2. By how much does the product 23 × 27 increase if only the second number (27) is increased by 1?

• A. 1
• B. 23
• C. 27
• D. 23 + 27

Q3. Using the distributive property, a(b + 1) is equal to which of the following?

• A. ab + 1
• B. ab + a
• C. a + b
• D. ab + b

Q4. Aarti draws a grid with a rows and (b + c) columns to picture a(b + c). She finds the total dots in two pieces of (b) and (c) columns. What does each piece represent?

• A. ab and ac
• B. a + b and a + c
• C. ab and bc
• D. b/a and c/a

Q5. An identity states that (a + m)(b + n) is equal to which expression?

• A. ab + mn
• B. ab + mb + an + mn
• C. a + b + m + n
• D. (a + m) + (b + n)

Q6. Ravi expands the product (3 + u)(v − 3). Using the distributive property, what does he get?

• A. 3v − 3u + uv − 9
• B. 3v + uv − 9
• C. 3v − 3u + uv + 9
• D. 3v − 3u − uv + 9

Q7. An identity gives the expansion of (a + b)^2. Which expression equals (a + b)^2?

• A. a^2 + b^2
• B. a^2 − 2ab + b^2
• C. a^2 + 2ab + b^2
• D. 2a + 2b

Q8. On Priya writes 65^2 as (60 + 5)^2 and uses Identity 1A. What value does she get?

• A. 3625
• B. 4225
• C. 3600 + 25
• D. 650

Q9. An identity gives the expansion of (a − b)^2. Which expression equals (a − b)^2?

• A. a^2 + 2ab + b^2
• B. a^2 + b^2
• C. a^2 − b^2
• D. a^2 − 2ab + b^2

Q10. Manju writes 55 = 60 − 5 and uses Identity 1B to compute 55^2. What value does she obtain?

• A. 3025
• B. 3625
• C. 3575
• D. 2975

Q11. An identity states the product of a sum and a difference. (a + b)(a − b) is equal to which expression?

• A. a^2 + 2ab + b^2
• B. a^2 − 2ab + b^2
• C. a^2 − b^2
• D. a^2 + b^2

Q12. Tenzin writes 98 × 102 as (100 − 2)(100 + 2) and uses Identity 1C. What product does he get?

• A. 9996
• B. 10000
• C. 9998
• D. 10004

Q13. Which mathematician gave the first explicit statement of the distributive property, in his work Brāhmasphuṭasiddhānta (verse 12.55) in 628 CE?

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

Q14. Like terms. Two terms in an algebraic expression are called 'like terms' when they have the same

• A. numerical coefficients
• B. letter-numbers (variables)
• C. signs
• D. number of digits

Q15. To multiply 3874 by 11 in a single step, the chapter splits 11 as (10 + 1) and uses the distributive property. The product 3874 × 11 equals

• A. 3874 + 11
• B. 38740 + 11
• C. 38740 + 3874
• D. 3874 × 10 × 1