How do you find the binomial expansion of #(x + 2)^4#?

1 Answer
Aug 17, 2015

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

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.

#(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4#

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

Let #y=2#.

Then your polynomial becomes

#(x+2)^4= (x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4#

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

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

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