You visited us 1 times! Enjoying our articles? Unlock Full Access!

Binomial Coefficients

Coefficient o...

Question

Coefficient of $x^{10}$ in $(1 + 2 x^{4}) (1 - x)^{8}$ is

-56

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

112

No worries! We‘ve got your back. Try BYJU‘S free classes today!

-112

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 56
$(1 + 2 x^{4}) (1 - x)^{8}$
$= (1 + 2 x^{4}) (1 - 8 x +^{8} C_{2} x^{2} -^{8} C_{3} x^{3} . . . +^{8} C_{2} x^{8})$
Hence coefficient of $x^{10}$ will be.
$2 \times^{8} C_{6} x^{4} (x^{6})$
Hence coefficient of $x^{10}$
$= 2^{8} C_{2}$
$= 2 (\frac{8 \times 7}{2})$
$= 56$

Suggest Corrections

Similar questions

x^{10}

-

x^{15}

{(1 + x + x^{2} + x^{3})}^{4} {(1 - x)}^{8}

x^{7}

(1 + x)^{10} + x (1 + x)^{9} + x^{2} (1 + x)^{8} + \dots + x^{10}

(1 - 2 x^{3} 3 x^{5}) (1 + \frac{1}{x})^{8}

x_{1}, x_{2}, x_{3}, . . . .

x_{1} + x_{7} + x_{10} = - 6

x_{3} + x_{8} + x_{12} = - 11

x_{3} + x_{8} + x_{22} = ?

x_{1}, x_{2}, x_{3}, . . .

x_{1} + x_{7} + x_{10} = - 6

x_{3} + x_{8} + x_{12} = - 11

x_{3} + x_{8} + x_{22}

Join BYJU'S Learning Program