How do you use the Binomial Theorem to expand (x + 1)^4?

2 Answers
May 2, 2018

x^4+4x^3+6x^2+4x+1

Explanation:

The binomial theorem states:
(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

so here, a=x and b=1

We get:
(x+1)^4 = x^4+4x^3(1)+6x^2(1)^2+4x(1)^3+(1)^4
(x+1)^4 = x^4+4x^3+6x^2+4x+1

May 2, 2018

1+4x+6x^2+4x^3+x^4

Explanation:

Binomial expansion is given by:
(a+bx)^n=sum_(r=0)^n(n!)/(r!(n-r)!)a^(n-r)(bx)^r

So, for (1+x)^4 we have:
(4!)/(0!(4-0)!)1^(4-0)x^0+(4!)/(1!(4-1)!)1^(4-1)x^1+(4!)/(2!(4-2)!)1^(4-2)x^2+(4!)/(3!(4-3)!)1^(4-3)x^3+(4!)/(4!(4-4)!)1^(4-4)x^4

1+4x+6x^2+4x^3+x^4