Question

desenvolva encontrando todos os termos

a (x+y)^3=?

b (x - y)^9=?

c (x + y)^4=?

me ajudem

Answer 1

a) $(x+y)^3$

$(x+y)^3=\dbinom{3}{0}x^{3}y^0+\dbinom{3}{1}x^{2}y^{1}+\dbinom{3}{2}x^{1}y^{2}+\dbinom{3}{3}x^{0}y^{3}$

$(x+y)^3=x^3+3x^2y+3xy^2+y^3$


b) $(x-y)^9$

$(x-y)^9=\dbinom{9}{0}x^{9}y^0-\dbinom{9}{1}x^{8}y^{1}+\dbinom{9}{2}x^{7}y^{2}-\dbinom{9}{3}x^{6}y^{3}+\dbinom{9}{4}x^{5}y^{4}-\dbinom{9}{5}x^{4}y^{5}\\+\dbinom{9}{6}x^{3}y^{6}-\dbinom{9}{7}x^{2}y^{7}+\dbinom{9}{8}x^{1}y^{8}-\dbinom{9}{9}x^{0}y^{9}$

$(x-y)^9=x^9-9x^8y+36x^7y^2-84x^6y^3+126x^5y^4-126x^4y^5+84x^3y^6-36x^2y^7\\+9xy^8-y^9$


c) $(x+y)^4$

$(x+y)^4=\dbinom{4}{0}x^{4}y^0+\dbinom{4}{1}x^{3}y^{1}+\dbinom{4}{2}x^{2}y^{2}+\dbinom{4}{3}x^{1}y^{3}+\dbinom{4}{4}x^{0}y^{4}$

$(x+y)=x^4+4x^3y+6x^2y^2+4xy^3+y^4$