Question

How can expressions be simplified using the distributive property? Choose the correct option below.

A) By distributing each term inside the parentheses to every term outside the parentheses.
B) By combining like terms within the parentheses and then distributing.
C) By multiplying each term inside the parentheses by the term outside the parentheses.
D) By adding the terms inside the parentheses and then distributing.

Answer 1

Expressions are simplified using the distributive property by multiplying each term inside the parentheses by the term outside. An example is A(B + C) = AB + AC. It's a handy tool for expanding and simplifying algebraic expressions.

Step-by-step explanation:

Expressions can be simplified using the distributive property by following option C: By multiplying each term inside the parentheses by the term outside the parentheses.

The distributive property allows for the multiplication of a single term by each of the terms in a sum or difference that is inside parentheses.

An example of this property is A(B + C) = AB + AC, where A is the term outside the parentheses being distributed across each term B and C inside the parentheses.

Here's a step-by-step example using the distributive property: Suppose you have 3(x + 2). To simplify this expression, you distribute the 3 to both x and 2, which results in 3 × x + 3 × 2.

After carrying out the multiplication, the expression simplifies to 3x + 6. The distributive property is a useful tool in algebra to expand and simplify expressions as part of the simplification process.