What is the binomial expansion of #(2x+1)^4#?

1 Answer
Aug 17, 2015

#color(red)((2x+1)^4 = 16x^4 + 32x^3 + 24x^2 + 8x + 1)#

Explanation:

Write out the fifth row of Pascal's triangle and make the appropriate substitutions.

Pascal's triangle is

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The numbers in the fifth row are 1, 4, 6, 4, 1.

They are the coefficients of the terms in a fourth order polynomial.

Your polynomial is #(2x+1)^4#

Let #y =2x#

Then your polynomial becomes

#(2x+1)^4= (y+1)^4#>

#(y+1)^4 = y^4 + 4y^3 + 6y^2 + 4y + 1#

If we substitute the value of #y#, we get

#(2x+1)^4 = (2x)^4 + 4(2x)^3 + 6(2x)^2 + 4(2x) + 1#

#(2x+1)^4 = 16x^4 + 32x^3 + 24x^2 + 8x + 1#