How do you use the binomial theorem to expand and simplify the expression $(x+1)^6$ ?

Question

15630 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-19T12:00:04

$(x+1)^6= x^6 + 6x^5+15x^4+20x^3+15x^2+6x+1$

Binomial theorem:
$(a + b)^n =(nC_0) a^nb^0+ (nC_1) a^(n-1)b^1 +(nC_2) a^(n-2)b^2 +...... (nC_n)a^0b^n$
Here $(a=x ; b=1 , n= 6) :. 1^n=1$

We know $nC_r= (n!)/(r!(n-r)!) :. 6C_0=1 , 6C_1=6 , 6C_2=15 ,6C_3=20, 6C_4=15, 6C_5=6, 6C_6=1$

$:. (x+1)^6= x^6 + 6x^5+15x^4+20x^3+15x^2+6x+1$ [Ans]

How do you use the binomial theorem to expand and simplify the expression (x+1)^6(x+1)^6?