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

Nov 5, 2016

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

Explanation:

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

$n p \left(n p - 1\right) \implies n p \cdot n p - n p \implies {n}^{2} {p}^{2} - n p$

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

$- 1 \left(n p - 1\right) \implies - n p + - 1 \cdot - 1 \implies - n p + 1$

Step 3) Add these two results together

${n}^{2} {p}^{2} - n p - n p + 1 \implies {n}^{2} {p}^{2} - 2 n p + 1$