Question

Determine which of the following situations requires the distributive property in order to simplify the expression. Select all situations that apply.

x(2y)
9(x ∙ y)
9(x + y)
(7 ∙ a)(b)
(7 - a)(b)
(2 ∙ x) ∙ y

Answer 1

9(x + y)

(7 - a)(b)

Explanation:

Answer 2

Answers

9(x + y)

(7 - a)(b)

The Distributive Property is used in algebraic expressions to multiply a single term and two or more terms which are inside a set of parentheses.

In the case of x(2y), there is only one term inside the parenthesis

In the case of 9(x ∙ y), the distributive property is not used because (x ∙ y) = xy which means only one term will be multiplied by the term outside the parenthesis (9)

In the case of 9(x + y), the distributive property is used because the two terms in the parenthesis (x and y) will be multiplied by the term outside the parenthesis (9)

9(x + y) = 9*x + 9*y (by applying the distributive property)

In the case of (7 ∙ a)(b), the distributive property is not used because (7 ∙ a) = 7a which means only one term will be multiplied by the term outside the parenthesis (b)

In the case of (7 - a)(b), the distributive property is used because the two terms in the parenthesis (7 and -a) will be multiplied by the term outside the parenthesis (b)

(7 - a)(b) = 7*b - a*b (by applying the distributive property)

In the case of (2 ∙ x) ∙ y, the distributive property is not used because (2 ∙ x) = 2x which means only one term will be multiplied by the term outside the parenthesis (y)