Distribute 4x(2y + 5).
The terms inside the parentheses are being added, not multiplied or divided, so we can distribute the 4x to each of them.
Distribute! Distribute like the wind!
4x(2y) + 4x(5)
Multiplying the coefficients and then the variables, we get our final answer.
8xy + 20x
Distribute -2xy(3x – z).
We need to distribute -2xy to 3x, but what about the z? How do we deal with two negative signs? Does that make the universe implode?
Nah, we can handle it. The universe is safe. Just distribute (or multiply) -2xy to 3x and to z, and leave a subtraction symbol between them.
(-2xy)(3x) – (-2xy)(z)
Now multiply everything. Remember, two negatives make a positive.
-6x2y + 2xyz
-z(-18 – z)
We now distribute -z to both -18 and -z, or multiply it by both of them.
-z(-18) + -z(-z)
Those double negatives turn into a positive, leaving us with 18z + z2.
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