# How do you use pascals triangle to expand  (2x-6)^7?

Aug 15, 2016

$128 {x}^{7} - 2688 {x}^{6} + 24192 {x}^{5} - \ldots \ldots . .$

#### Explanation:

Using $\textcolor{b l u e}{\text{Pascal's triangle}}$

here n = 7 : using the coefficients from the 7th row.

That is $\textcolor{red}{1 , 7 , 21 , 35 , 35 , 21 , 7 , 1}$

with decreasing powers of 2x from ${\left(2 x\right)}^{7} \to {\left(2 x\right)}^{0}$

and increasing powers of -6 from ${\left(- 6\right)}^{0} \to {\left(- 6\right)}^{7}$

${\left(2 x - 6\right)}^{7} = 1 \times {\left(2 x\right)}^{7} {\left(- 6\right)}^{0} + 7 \times {\left(2 x\right)}^{6} {\left(- 6\right)}^{1} + 21 \times {\left(2 x\right)}^{5} {\left(- 6\right)}^{2} + \ldots \ldots$

$= 128 {x}^{7} - 2688 {x}^{6} + 24192 {x}^{5} - \ldots \ldots .$

The remaining terms can be calculated in the same way.