How do you multiply $(n p - 1) (n p - 1)$ $(np-1)(np-1)$ ?

Question

1306 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-05T12:33:18

$n^{2} p^{2} - 2 n p + 1$ $n^2p^2 - 2np + 1$

Step 1) Multiple the first element ( $n p$ $np$ ) in the left term by the right term.

$n p (n p - 1) \Rightarrow n p \cdot n p - n p \Rightarrow n^{2} p^{2} - n p$ $np(np - 1) => np*np - np => n^2p^2 - np$

Step 2) Multiple the second element ( $- 1$ $-1$ ) in the left term by the right term.

$- 1 (n p - 1) \Rightarrow - n p + - 1 \cdot - 1 \Rightarrow - n p + 1$ $-1(np - 1) => -np + -1*-1 => -np + 1$

Step 3) Add these two results together

$n^{2} p^{2} - n p - n p + 1 \Rightarrow n^{2} p^{2} - 2 n p + 1$ $n^2p^2 - np -np + 1 => n^2p^2 - 2np + 1$

How do you multiply (np-1)(np-1)(np−1)(np−1)(np-1)(np-1)?