Question

In which of the following examples is the distributive property used correctly? Select all that apply.

A. 8(4d + 3q) = 32d + 24q
B. 4(m + 9g) = 4m + 36g
C. 7(2c + 5b) = 14c × 35b
D. 9(6f + 7j) = 63f + 72j

Answer 1

Options A, B, and D correctly use the distributive property, which states that A(B+C) should be expanded to AB + AC. Option C is incorrect as it applied multiplication incorrectly.

Step-by-step explanation:

The distributive property in mathematics is used to multiply a single term and two or more terms inside a set of parentheses. The standard form of the distributive property is A(B+C) = AB + AC. Using this property, we can determine which of the given examples correctly apply the distributive property.

A. 8(4d + 3q) = 32d + 24q is correct because each term inside the parentheses is multiplied by 8.

B. 4(m + 9g) = 4m + 36g is also correct as the distributive property is applied correctly to both terms inside the parentheses, multiplying them by 4.

C. 7(2c + 5b) = 14c × 35b is incorrect because the distributive property was applied incorrectly by multiplying the two terms together instead of distributing the 7 to each term.

D. 9(6f + 7j) = 63f + 72j is correct because 9 is properly distributed to 6f and 7j, resulting in 63f and 72j, respectively.

Answer selections A, B, and D correctly use the distributive property.

Answer 2

The distributive property is correctly used in examples A, B, and D. Example C incorrectly uses multiplication instead of addition after distributing the term.

Step-by-step explanation:

The distributive property in mathematics is used to multiply a single term and two or more terms inside a set of parentheses. The correct application of the distributive property can be defined as A(B + C) = AB + AC. When looking at the examples provided:

• Example A: 8(4d + 3q) = 32d + 24q is correct because each term inside the parentheses is multiplied by the factor outside, 8.
• Example B: 4(m + 9g) = 4m + 36g is correct for the same reason as A; the factor 4 is distributed correctly to both m and 9g.
• Example C: 7(2c + 5b) = 14c × 35b is incorrect because instead of using addition between the two distributed terms, a multiplication sign is incorrectly used in the answer.
• Example D: 9(6f + 7j) = 63f + 72j is correct, as the factor 9 is distributed to both 6f and 7j, and the answers are added together as per the distributive property.

Therefore, the examples that use the distributive property correctly are A, B, and D.