How do you find the coefficient of $x^4$ in the expansion of $(x+2)^8$ ?

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Answer 1 · 2017-05-31T12:14:07

Co-efficient of $x^4$ is $1120$

$(x+2)^8= x^8+nc_1x^7*2^1+nc_2x^6*2^2+nc_3x^5*2^3+ nc_4x^4*2^4+..............+2^8$

Co-efficient of $x^4$ is $nc_4*2^4 = (8!)/(4!*4!)*16=70*16=1120$ [Ans]

How do you find the coefficient of x^4x^4 in the expansion of (x+2)^8(x+2)^8?