Question

Find the coefficient of x33
of the binomial (x3 + x4)10​

Answer 1

x33

therefore ,

10c0 (x³) 10

10c1 ( x³) 3 × X⁴

10c2 (x³) 8 × (x⁴) 2

10c3 (x³) 7 × (x⁴) 3

hence , 10c3x³³

10c3 = 10 × 9× 8 × 7! / 3! × 7 !

720/6 = 120

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Answer 2

The Coefficient of x³³ is 120.

Given,

Binomial expression → (x³ + x⁴)¹⁰

To Find,

Coefficient of x³³

Solution,

The term (x³ + x⁴)¹⁰ can be written as -

⇒ [x³(1 + x)]¹⁰

⇒ x³⁰(1 + x)¹⁰

The general term for binomial expression is -

ⁿCr * $a^n^-^r$ * $b^r$

The general term for this expression would be -

x³⁰ * (¹⁰Cr * $1^1^0^-^r$ * $x^r$)

Now the required term is x³³, but x³⁰ is already present. Thus we require the term x³ from the binomial expression.

⇒ r becomes 3

Coefficient of x³³ = x³⁰ * (¹⁰C₃ * $1^1^0^-^3$ * $x^3$)

Coefficient of x³³ = ¹⁰C₃ * $1^7$

Coefficient of x³³ =  $\frac{10!}{3!7!}$ * $1^7$

Coefficient of x³³ = $\frac{10*9*8*7!}{3*2 * 7!}$

Coefficient of x³³ = $\frac{10*9*8}{3*2}$

Coefficient of x³³ = $\frac{720}{6}$

Coefficient of x³³ = 120

Therefore, the coefficient is 120.

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