Question

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

Answer:

ANSWER

The coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+x³)⁴ is equal to

the coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+4x³+6x⁶+4x⁹)

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

+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,

Coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³=0, since the highest degree term in the expansion is 8.

Coefficient of x⁷ in the expansion of (1+x)²(1+x²)³=

Coefficient of x⁷ in the expansion of (1+2∗x+x²)(1+x²)³

=2∗Coefficient of x⁶ in the expansion of (1+x²)³

=2∗1=2,

Coefficient of x⁴ in the expansion of (1+x)²(1+x²)³=

Coefficient of x⁴ in the expansion of (1+2∗x+x²)(1+x²)³

=1*Coefficient of x⁴ 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)⁴

=0+4∗2+6∗6+4∗2

1. =52.