Question

the value of (2/3)³ ×(1/2)⁴ is
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Answer 1

The coefficient of x¹0 in the expansion of (1+x)(1+x²)³(1+x³)4 is equal to

the coefficient of x¹0 in the expansion of 10 (1+x)(1+x2)³(1+4x³+6x6+4x³)

We can ignore the last term in the expansion (1+x³)4, since its exponent is

greater than 10.

= Coefficient of x¹0 in the expansion of (1+x)²(1+x²)³ 10

+4*Coefficient of x7 in the expansion of

(1+x)²(1+x²)³

+6*Coefficient of x4 in the expansion of

(1+x)²(1+x²)³

+4*Coefficient of x in the expansion of (1+x)²(1+x²)³,

=1'Coefficient of x in the expansion of $ $(1+x²)³ +

1"Coefficient of x in the expansion of (1+x²)³

=3+3=6

Coefficient of x in the expansion of (1+2*x+x²)(1+x²)³

=2* constant in the expansion of (1+x²)³

=2,

Thus the coefficient of x¹0 in the expansion of (1+x)²(1+x²)³(1+x³)

=0+4+2+6+6+4+2

1. = 52

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Answer 2

Answer:

Step-by-step explanation:

$( \frac{2}{3} )^3 * ( \frac{1}{2} )^4\\\\\frac{8}{27} * \frac{1}{16}\\\\\frac{8}{432}$