(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.
