Question

verify x³+y³= (x+y)(x²-xy+y²)​

Answer 1

Answer:

Hey there !

We have to prove that x³ - y³ = (x-y)(x² + xy + y²)

So, Let's take R. H. S and prove it equal to L.H. S.

R. H. S

= (x-y)(x² + xy + y²)

= x ( x² + xy + y² ) - y ( x² + xy + y²)

= x³ + x²y + xy² -yx² -xy² - y³

= x^3 + \cancel{ x^2 y } + \cancel{ x y^2 } - \cancel{ x^2 y } - \cancel{ x y^2 } -y^3x

3

+

x

2

y

+

xy

2

−

x

2

y

−

xy

2

−y

3

= x³ - y³

= L. H. S.

\begin{gathered}\mathbf{ Therefore \: , \: We \: proved \: that } \\ \boxed{x^3 - y^3 = (x-y)(x^2 + xy + y^2 ) \: }\end{gathered}

Therefore,Weprovedthat

x

3

−y

3

=(x−y)(x

2

+xy+y

2

)