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

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)