7.13.1 Equivalent Expressions

Algebra 17.13.1 Equivalent Expressions

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Warm Up

Complete each row with an equivalent expression in standard form or factored form.

Standard Form	Factored Form
$x^{2}$	a. _____
d. _____	$x (x + 9)$
$x^{2} - 18 x$	b. _____
e. _____	$x (6 - x)$
$- x^{2} + 10 x$	c. _____
f. _____	$- x (x + 2.75)$

a. What is the factored form of $x^{2}$ ?

Compare your answer:

$x \cdot x$

b. What is the factored form of $x^{2} - 18 x$ ?

Compare your answer:

$x (x - 18)$

c. What is the factored form of $- x^{2} + 10 x$ ?

Compare your answer:

$- x (x - 10)$ or $x (- x + 10)$ or $x (10 - x)$

d. What is the standard form of $x (x + 9)$ ?

Compare your answer:

$x^{2} + 9 x$

e. What is the standard form of $x (6 - x)$ ?

Compare your answer:

$- x^{2} + 6 x$

f. What is the standard form of $- x (x + 2.75)$ ?

Compare your answer:

$- x^{2} - 2.75 x$

2. What do the quadratic expressions in each column have in common (besides the fact that everything in the left column is in standard form and everything in the other column is in factored form)? Be prepared to share your observations.

Compare your answer:

In the left column, all the expressions in standard form have a squared term and a linear term but no constant term, and the squared term has a coefficient of either 1 or -1. In the right column, one of the factors is just a variable whose coefficient is 1 or -1, and the other factor is either a sum or a difference.

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
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- Section URL: https://openstax.org/books/algebra-1/pages/7-13-1-equivalent-expressions

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