Apply the distributive property to expand expressions

The distributive property establishes that a factor multiplied by a sum or difference multiplies each term: $a(b+c)=ab+ac$ and $a(b-c)=ab-ac$ . Mastery includes expanding linear expressions with integer or rational coefficients, including negative factors, while preserving equivalent values and distinguishing terms from factors; the factor must be applied to every term inside the parentheses, not only the first. Products of two multi-term polynomials and more advanced polynomial techniques are outside this scope.

Detailed Explanation: Apply the distributive property to expand expressions

The distributive property means that a factor outside parentheses must be multiplied by every term inside:

a(b+c)=ab+ac \qquad\text{and}\qquad a(b-c)=ab-ac

Example

Expand:

-3(2x-5)

Step 1: Identify the factor and the terms.

The factor outside the parentheses is $-3$ .
The terms inside are $2x$ and $-5$ .

Step 2: Multiply $-3$ by each term.

-3(2x-5)=(-3)(2x)+(-3)(-5)

Step 3: Simplify each product.

(-3)(2x)=-6x

and

(-3)(-5)=15

So the expanded expression is

\boxed{-6x+15}

Remember: distribute the outside factor to every term inside the parentheses, including terms with negative signs.

Learn by doing: Apply the distributive property to expand expressions

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Algebraic Functions - Value Times Bracketed Terms

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