Question

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

Answer 1

`128x^7-2688x^6+24192x^5- ........`

Explanation:

Using `color(blue)"Pascal's triangle"`

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

That is `color(red)(1,7,21,35,35,21,7,1)`

with decreasing powers of 2x from `(2x)^7to(2x)^0`

and increasing powers of -6 from `(-6)^0to(-6)^7`

`(2x-6)^7=1xx(2x)^7(-6)^0+7xx(2x)^6(-6)^1+21xx(2x)^5(-6)^2+ ......`

`=128x^7-2688x^6+24192x^5- .......`

The remaining terms can be calculated in the same way.