Mini Lesson Question

Which expression is equivalent to

(x – 3) (x + 4)

?

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.

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

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. $x^{2} - 5 x - 14$

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

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

Check yourself:
Begin by distributing the first binomial to each term in the second binomial.
$x (x - 1) + 5 (x - 1)$

Then, distribute the factors into each set of parentheses and simplify.
$x 2 - x + 5 x - 5 = x^{2} + 4 x = 5$

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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