(1-x+x^2)^4

It is bionomial theorem's quetion.Solve it by expansion
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1 Answer

(1-x+x^2)^4=(1-x(1-x))^4.
Coefficients are 1 4 6 4 1 (Pascal and binomial).
Also: (1-x)^2=1-2x+1 and (1-x)^3=1-3x+3x^2-x^3
Terms: 1-4x(1-x)+6x^2(1-x)^2-4x^3(1-x)^3+x^4(1-x)^4
1-4x+4x^2+6x^2-12x^3+6x^4-4x^3+12x^4-12x^5+4x^6+x^4-4x^5+6x^6-4x^7+x^8.
1-4x+10x^2-16x^3+19x^4-16x^5+10x^6-4x^7+x^8.
by Top Rated User (1.2m points)

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