How do you use pascals triangle to expand (x-5)^6?

Aug 17, 2015

${x}^{6} - 30 {x}^{5} + 375 {x}^{4} - 2500 {x}^{3} + 9375 {x}^{2} - 18750 x + 15625$

Explanation:

Since the binomial is taken to the 6th power we need the 6th row of Pascal's triangle. This is:

$1 - 6 - 15 - 20 - 15 - 6 - 1$

These are the co-effiecents for the terms of the expansion, giving us:

${x}^{6} + 6 {x}^{5} \left(- 5\right) + 15 {x}^{4} {\left(- 5\right)}^{2} + 20 {x}^{3} {\left(- 5\right)}^{3} + 15 {x}^{2} {\left(- 5\right)}^{4} + 6 x {\left(- 5\right)}^{5} + {\left(- 5\right)}^{6}$

This evaluates to:
${x}^{6} - 30 {x}^{5} + 375 {x}^{4} - 2500 {x}^{3} + 9375 {x}^{2} - 18750 x + 15625$