Question

Expand the expression:
a) (u + v)^3
b) (u + v)^4

Answer 1

(a)
`(a+b)^3=a^3+b^3+3ab(a+b)=a^3+b^3+3a^2b+3ab^2`

(b)
`(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`

Explanation:

We have to expand the expression

(a)
`(u+v)^3` there are different methods for expanding the expression here u used algebraic identity for expansion

We know the algebraic identity

`(a+b)^3=a^3+b^3+3ab(a+b)=a^3+b^3+3a^2b+3ab^2`

(b)
`(u+v)^4`

We know the algebraic identity
`(a+b)^2=a^+b^2+2ab`

`(u+v)^4` can be written as
`(u+v)^2* (u+v)^2`

`(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`