Question

Desenvolver (x+1) elevado a 7

Answer 1

= (x+1)^7

= (x+1)^3.(x+1)^2.(x+1)^2

= (x+1).(x+1)^2. (x^2+2x+1).(x^2+2x+1)

(A)

= (x+1).(x^2+2x+1)

= x^3 + 2x^2 + x + x^2 + 2x + 1

= x^3 + 3x^2 + 3x + 1

(B)

= (x^2+2x+1).(x^2+2x+1)

= x^4 + 2x^3 + x^2 + 2x^3 + 4x^2 + 2x + x^2 + 2x + 1

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

= a . b

= (x^3 + 3x^2 + 3x + 1). (x^4 + 4x^3 + 6x^2 + 4x + 1)

= x^7 + 4x^6 + 6x^5 + 4x^4 + x^3 + 3x^6 + 12x^5 + 18x^4 + 12x^3 + 3x^2 + 3x^5 + 12x^4 + 18x^3 + 12x^2 + 3x + x^4 + 4x^3 + 6x^2 + 4x + 1

= x^7 + 7x^6 + 21x^5 + 35x^4 + 35x^3 + 21x^2 + 7x + 1