Respuesta :
Answer:
(a) [tex](a+b)^3=a^3+b^3+3ab(a+b)=a^3+b^3+3a^2b+3ab^2[/tex]
(b) [tex](u^2+v^2+2uv )(u^2+v^2+2uv)=u^4+u^2v^2+2u^3v+u^2v^2+v^4+2uv^3+2u^3v+2uv^3+4u^2v^2=u^4+v^4+4u^3v+4v^3u+5u^2v^2[/tex]
Step-by-step explanation:
We have to expand the expression
(a) [tex](u+v)^3[/tex] there are different methods for expanding the expression here u used algebraic identity for expansion
We know the algebraic identity
[tex](a+b)^3=a^3+b^3+3ab(a+b)=a^3+b^3+3a^2b+3ab^2[/tex]
(b) [tex](u+v)^4[/tex]
We know the algebraic identity [tex](a+b)^2=a^+b^2+2ab[/tex]
[tex](u+v)^4[/tex] can be written as [tex](u+v)^2\times (u+v)^2[/tex]
[tex](u^2+v^2+2uv )(u^2+v^2+2uv)=u^4+u^2v^2+2u^3v+u^2v^2+v^4+2uv^3+2u^3v+2uv^3+4u^2v^2=u^4+v^4+4u^3v+4v^3u+5u^2v^2[/tex]
