Question

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

Answer 1

Answer:

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

(b) $(u^2+v^2+2uv )(u^2+v^2+2uv)=u^4+u^2v^2+2u^3v+u^2v^2+v^4+2uv^3+2u^3v+2uv^3+4u^2v^2=u^4+v^4+4u^3v+4v^3u+5u^2v^2$                        

Step-by-step 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 $(u+v)^2\times (u+v)^2$

$(u^2+v^2+2uv )(u^2+v^2+2uv)=u^4+u^2v^2+2u^3v+u^2v^2+v^4+2uv^3+2u^3v+2uv^3+4u^2v^2=u^4+v^4+4u^3v+4v^3u+5u^2v^2$