Write Equivalent Expressions: Mini-Lesson Review

Algebra 1Write Equivalent Expressions: Mini-Lesson Review

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Mini Lesson Question

Which expression is equivalent to

(x – 3) (x + 4)

$x^2-3x-12$
$x^2-x-12$
$x^2+x-12$
$x^2+4x$

Write Equivalent Expressions Using the Distributive Property

The standard form of a quadratic expression is $a x^{2} + b x + c$ , where $a$ , $b$ , and $c$ are constants, and $a$ is not 0.

Example

Write $(x - 3) (x + 5)$ as an equivalent expression in standard form using the distributive property.

Step 1 - Multiply each term in the first binomial by the second binomial.

$(x - 3) (x + 5)$

$x (x + 5) - 3 (x + 5)$

Step 2 - Use the distributive property to eliminate the parentheses.

$x^{2} + 5 x - 3 x - 15$

Step 3 - Combine like terms.

$x^{2} + 2 x - 15$

Try it

Try It: Write Equivalent Expressions Using the Distributive Property

Write $(x + 2) (x - 7)$ as an equivalent expression in standard form using the distributive property.

Here is how to write equivalent expressions using the distributive property:

Step 1 - Multiply each term in the first binomial by the second binomial. $(x + 2) (x - 7)$ $x (x - 7) + 2 (x - 7)$

Step 2 - Use the distributive property to eliminate the parentheses. $x^{2} - 7 x + 2 x - 14$

Step 3 - Combine like terms. $x^{2} - 5 x - 14$

Check Your Understanding

Which expression is equivalent to $(x + 5) (x - 1)$ ?

Multiple Choice:

$x^{2} + 4 x - 5$
$x^{2} - 4 x + 5$
$x^{2} + 5 x - 1$
$x^{2} + 5 x - 5$

$x^{2} + 4 x - 5$

Video: Multiplying Binomials

Watch the following video to learn more about multiplying binomials using the distributive property to write equivalent expressions.

Khan Academy: Multiplying Binomials

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- 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/8-write-equivalent-expressions-mini-lesson-review

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