Solve this: Q) Find the coefficient of x2y4z2 in the expansion of 2x-3y+4z9 - Maths - Binomial Theorem

Question

Solve this:
Q) Find the coefficient of x 2 y 4 z 2 in the expansion of 2 x - 3
y + 4 z 9

Neha Sethi · Accepted Answer

Dear student
Sol:  General term in 2x-3y+4z9=9!n1!×n2!×n3!×2xn1-3yn24zn3=9!n1!×n2!×n3!×2n1-3n24n3×xn1 yn2 zn3Putting n1=3,n2=4, n3=2=9!3!×4!×2!×23-3442×x3 y4 z2=9×8×7×6×5×4!3 ×2×1×4!×2×1×8×81×16×x3 y4 z2⇒coefficient of x3 y4 z2=9×8×7×5×81×8×8=13063680

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Solve this: Q). Find the coefficient of x 2 y 4 z 2 in the expansion of 2 x - 3 y + 4 z 9 .

Solve this:
Q). Find the coefficient of $x^{2} y^{4} z^{2}$ in the expansion of ${(2 x - 3 y + 4 z)}^{9}$ .