How do I use Pascal's triangle to expand a binomial?

1 Answer
Oct 31, 2015

Answer:

Rows of Pascal's triangle provide the coefficients to expand #(a+b)^n# as follows...

Explanation:

To expand #(a+b)^n# look at the row of Pascal's triangle that begins #1, n#. This provides the coefficients.

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For example, #(a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4# from the row #1, 4, 6, 4, 1#

How about #(2x-5)^4# ?

Let #a = 2x# and #b = -5#.

Then:

#(2x-5)^4 = (a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4#

#=(2x)^4+4(2x)^3(-5)+6(2x)^2(-5)^2+4(2x)(-5)^3+(-5)^4#

#=16x^4+4(8x^3)(-5)+6(4x^2)(25)+4(2x)(-125)+(625)#

#=16x^4-160x^3+600x^2-1000x+625#