Use the Binomial Theorem to expand (x+7)^4 and express the result in simplified form?

1 Answer
1s2s2p
May 17, 2018

2401+1372x+294x^2+28x^3+x^4

Explanation:

Using binomial theorem we can express (a+bx)^c as an expanded set of x terms:
(a+bx)^c=sum_(n=0)^c(c!)/(n!(c-n)!)a^(c-n)(bx)^n

Here, we have (7+x)^4

So, to expand we do:
(4!)/(0!(4-0)!)7^(4-0)x^0+(4!)/(1!(4-1)!)7^(4-1)x^1+(4!)/(2!(4-2)!)7^(4-2)x^2+(4!)/(3!(4-3)!)7^(4-3)x^3+(4!)/(4!(4-4)!)7^(4-4)x^4

(4!)/(0!(4-0)!)7^4x^0+(4!)/(1!(4-1)!)7^3x^1+(4!)/(2!(4-2)!)7^2x^2+(4!)/(3!(4-3)!)7x^3+(4!)/(4!(4-4)!)7^0x^4

(4!)/(0!4!)7^4+(4!)/(1!3!)7^3x+(4!)/(2!2!)7^2x^2+(4!)/(3!1!)7x^3+(4!)/(4!0!)x^4

7^4+4(7)^3x+24/4 7^2x^2+4(7)x^3+x^4

2401+1372x+294x^2+28x^3+x^4

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