The coefficient of x10 in the expansion of (1+x)2(1+x2)3(1+x3)4 is equal to :
Answers
Answer:
52
Step-by-step explanation:
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
=52.
Answer:
52
Step-by-step explanation:
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
=52.