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

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May 2, 2018

Answer:

#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#

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May 2, 2018

Answer:

#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#

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