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

1 Answer
Jim G.
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.

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