Question

factorise a^9+b^9+3a^6b^3+3a^3b^6

Answer 1

\(\large\tt \color{blue}{put~~a^3=x~and~b^3=y}\)


\(\large\tt \color{black}{= (x^3+y^3+3x^2y+3xy^2)}\)


\(\large\tt \color{black}{= (x^3+x^2y+2x^2y+2xy^2+xy^2+y^3)}\)


\(\large\tt \color{black}{= [x^2(x+y)+2xy(x+y)+y^2(x+y)]}\)


\(\large\tt \color{black}{= [(x+y)(x^2+2xy+y^2)]}\)


\(\large\tt \color{black}{= (x+y)(x+y)^2}\)


\(\large\tt \color{black}{= (x+y)^3}\)


\(\large\tt \color{blue}{put~back~~x=a^3~andy=b^3}\)


\(\large\tt \color{black}{= (a^3+b^3)^3}\)