Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

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Algebra 1

Simplify Expressions Using the Distributive Property: Mini-Lesson Review

Algebra 1Simplify Expressions Using the Distributive Property: Mini-Lesson Review

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Mini Lesson Question

Question #2: Simplify Expressions Using the Distributive Property

Which expression is equivalent to

-2(x-4)

$2x-8$
$-2x+8$
$-2x-8$
$-2x-4$

Simplify Expressions Using the Distributive Property

The Distributive Property can be used to remove parentheses as you simplify expressions.

DISTRIBUTIVE PROPERTY

$\begin{matrix} If a, b, c are real numbers, then & a (b + c) = a b + a c \\ Also, & (b + c) a = b a + c a \\ a (b - c) = a b - a c \\ (b - c) a = b a - c a \end{matrix}$

Simplify:

1. $3 (x + 4)$

It may help to use arrows to show the Distributive Property.

Use the Distributive Property.

$3 \cdot x + 3 \cdot 4$

Multiply.

$3 x + 12$

2. $- 11 (4 - 3 a)$

Use arrows to show the Distributive Property.

Use the Distributive Property

$- 11 \cdot 4 - (- 11) \cdot 3 a$

Multiply.

$- 44 - (- 33 a)$

Simplify.

$- 44 + 33 a$

Watch signs when using the Distributive Property with negative signs.

Try it

Try It: Simplify Expressions Using the Distributive Property

Simplify: $- 2 (4 y + 1)$ .

Here is how to simplify expressions using the Distributive Property.

Use arrows to show the Distributive Property.

Use the Distributive Property.

$- 2 \cdot 4 y + (- 2) \cdot 1$

Multiply.

$- 8 y + (- 2)$

Simplify.

$- 8 y - 2$

Check Your Understanding

Which expression is equivalent to $4 (5 - 2 a)$ ?

Multiple Choice:

$20 - 2 a$
$20 + 2 a$
$20 - 8 a$
$20 + 8 a$

Check yourself: Multiply the factor outside the parentheses by each term inside the parentheses.

Videos: Using the Distributive Property to Simplify Expressions

Watch the first 2 minutes and 40 seconds of the video to see how to use the Distributive Property to simplify expressions.

Khan Academy: Distributive property with variables

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Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/6-simplify-expressions-using-the-distributive-property-mini-lesson-review

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.