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

1 Answer
Aug 15, 2016

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

Explanation:

Using color(blue)"Pascal's triangle"
enter image source here

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.