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#
