Apply the distributive property to expressions

The distributive property explains that a factor multiplied by a sum or difference multiplies every term: $a(b+c)=ab+ac$ and $a(b-c)=ab-ac$ . Learners apply this relationship to numerical factors and simple one-variable expressions to produce equivalent forms, interpreting expanded expressions as the same total quantity and avoiding the misconception that the factor applies only to the first term; more advanced polynomial expansion and generalized coefficient systems are outside this scope.

Detailed Explanation: Apply the distributive property to expressions

The distributive property means that a factor outside parentheses is multiplied by each term inside the parentheses.

For a sum:

a(b+c)=ab+ac

For a difference:

a(b-c)=ab-ac

Example

Simplify:

3(x+4)

Step 1: Identify the factor outside the parentheses.

The factor is $3$ .

Step 2: Multiply $3$ by each term inside the parentheses.

3(x+4)=3\cdot x+3\cdot 4

Step 3: Simplify the products.

3\cdot x=3x \qquad\text{and}\qquad 3\cdot 4=12

So,

\boxed{3(x+4)=3x+12}

The $3$ must be used with both $x$ and $4$ . This keeps the expression equivalent, meaning $3(x+4)$ and $3x+12$ always have the same value.

Learn by doing: Apply the distributive property to expressions

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Algebraic Functions - Value Times Bracketed Terms

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