Skill: Expand expressions using distribution

Explanation and Free Practice Resources

Expansion interprets multiplication across a sum or difference: a factor outside parentheses multiplies every term inside, so expressions such as $3(x+4)$ and $3x+12$ have the same value for every $x$ . The reasoning applies the distributive property with simple one-variable expressions and whole-number or familiar rational coefficients, including attention to subtraction; it does not extend to multiplying two multi-term polynomials or more advanced symbolic cases.

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Detailed Explanation: Expand expressions using distribution

To expand an expression, multiply the factor outside the parentheses by every term inside the parentheses.

For example, expand:

4(x-3)

Multiply $4$ by the first term, $x$ :

4\cdot x=4x

Multiply $4$ by the second term, $-3$ :

4\cdot(-3)=-12

Write the results together:

4(x-3)=4x-12

So, the expanded expression is:

\boxed{4x-12}

Remember: the outside factor must be multiplied by each term inside the parentheses, including a negative term.

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Algebraic Functions - Value Times Bracketed Terms

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