Distribution

Multiplication distributes over Addition.

9 * (2 + 1 ) = (9*2) + (9*1)

9* (3) = (18) + (9)

27 = 27

True

Illustration of 9 distributed over 1 and 2.
  • Multiplication Distributes over Addition (True)
  • Addition Distributes over Multiplication (False)

Let’s try the reverse of what was done, to see what happens when we try to distribute addition over multiplication:

9 + (2 * 1 ) = (9+2) * (9+1)

9 + (2) = (11) * (10)

11 = 21

False

Appendix A

Look at the example below:

2 * (\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} + \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix} )= 2 * \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} + 2 * \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}

Appendix B

Example with Einstein notation:

a_i*(b_i+c_i) = a_ib_i + a_ic_i