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Find the 4th term of (x+2)^10

User Cnherald
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1 Answer

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(x + 2)¹⁰

Would take the terms in reducing powers of x, and increasing powers of 2.


1st term = ¹⁰C₀ x¹⁰(2)⁰ = x¹⁰

Second term = ¹⁰C₁ x¹⁰⁻¹(2)¹ = ¹⁰C₁ x⁹(2)¹

Third term = ¹⁰C₂ x¹⁰⁻²(2)² = ¹⁰C₂ x⁸(2)²

Fourth term = ¹⁰C₃ x¹⁰⁻³(2)³ = ¹⁰C₃ x⁷(2)³


So we shall now simplify the fourth term which is = ¹⁰C₃ x⁷(2)³

ⁿCr = n! /( r!(n -r)! )

¹⁰C₃ = 10! /( 3!(10 -3)! ) = 10! / (3!*7!) = (10 *9 * 8* 7!) / (3!*7!)

= 10*9*8 / 3! = (10*9*8) / (3*2*1) = 120


4th term = ¹⁰C₃ x⁷(2)³ = 120 *x⁷*(2)³ = 120*2³*x⁷

= 120*8x⁷

= 960x⁷

So the fourth term in reducing powers of x = 960x⁷

I hope this helped.

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