Which of the following correctly shows the application of the distributive property to the expression (7i - 8) (-2i - 5)?
To apply the distributive property to the expression (7i - 8)(-2i - 5), you need to distribute each term in the first parentheses to each term in the second parentheses. Here's how it would look:
(7i - 8)(-2i - 5) = (7i)(-2i) + (7i)(-5) + (-8)(-2i) + (-8)(-5)
Therefore, the correct application of the distributive property is:
(7i - 8)(-2i - 5) = -14i² - 35i + 16i + 40
Now, simplify further:
= -14i² - 19i + 40
Thus, the expression (7i - 8)(-2i - 5) correctly applies the distributive property to give -14i² - 19i + 40.
To apply the distributive property to the expression (7i - 8) (-2i - 5), we need to distribute both terms in the first expression to both terms in the second expression. Let's break it down step-by-step:
Step 1: Distribute the first term in the first expression (-2i) to both terms in the second expression:
(-2i) * (-2i) = 4i^2 = 4(-1) = -4
(-2i) * (-5) = 10i
Step 2: Distribute the second term in the first expression (-5) to both terms in the second expression:
(-5) * (-2i) = 10i
(-5) * (-5) = 25
Now, let's combine these results:
-4 + 10i + 10i + 25
Simplifying further, we combine like terms:
-4 + 20i + 25
Finally, combining the remaining terms:
21 + 20i
Therefore, the correct application of the distributive property is (7i - 8) (-2i - 5) = 21 + 20i.
To apply the distributive property to the given expression (7i - 8) (-2i - 5), you need to distribute each term from the first expression to each term in the second expression. Here are the steps:
1. Multiply the first term of the first expression (7i) by each term in the second expression (-2i and -5):
a. Multiply 7i by -2i: (7i) * (-2i) = -14i^2 (Remember that i^2 is equal to -1)
b. Multiply 7i by -5: (7i) * (-5) = -35i
2. Multiply the second term of the first expression (-8) by each term in the second expression (-2i and -5):
a. Multiply -8 by -2i: (-8) * (-2i) = 16i
b. Multiply -8 by -5: (-8) * (-5) = 40
3. Combine the results from steps 1 and 2 to get the final expression:
-14i^2 - 35i + 16i + 40
Now, you can simplify the expression further if needed.