In this lesson we will explore one of the most important properties of all:
 

4(3x + 5y - 6z)
Do you see that this is an example of multiplying a monomial (the 4)
by a polynomial? (3x + 5y -6z).
The distributive property works like this:
Multiply every term inside the parentheses by the monomial
in front of the parentheses.
As always, be very careful to use the rules for multiplying signed numbers!
 

4(3x + 5y - 6z) =
4(3x) + 4(5y) - 4(6z) =
12x + 20y - 24z

5x(3a - 7b -6c + 8d) =
5x(3a) -5x(7b) -5x(6c) +5x(8d) =
15ax - 35bx - 30cx +40dx

4x²y(2x²y³ +8x⁶y - 7xy⁷) =
4x²y(2x²y³) + 4x²y(8x⁶y) - 4x²y(7xy⁷) =
8x⁴y⁴ + 32x⁸y² -28x³y⁸
 

Let's Practice
  Click Here