Question

Use the Distributive Property to find (z−5)(z+3).

Answer 1

The Distributive Property allows you to multiply the terms within (z−5)(z+3) to obtain z² + 3z - 5z - 15. After combining like terms, the final result is z² - 2z - 15.

Step-by-step explanation:

To use the Distributive Property to find the product of (z−5)(z+3), you multiply each term in the first parenthesis by each term in the second parenthesis. Here are the steps:

Multiply z by z, which is z².

Multiply z by +3, which gives you +3z.

Multiply -5 by z, which results in -5z.

Finally, multiply -5 by +3, which is -15.

After multiplication, you combine like terms:

z² + 3z - 5z - 15

Combine +3z and -5z to get -2z

So, the final result is z² - 2z - 15.

Answer 2

Consider,
`(z-5)(z+3)`. Let's say
`a = z-5` then the problem reduces to
`a(z+3)=za+3a`. (Do you understand this step?)

So then replacing a again with our definition we get,
`z(z-5)+3(z-5)=z^2-5z+3z-15=z^2-2z-15`.