Question

prove that x^3+y^3 (x+y)(x^2+y^2-xy​)

Answer 1

Step-by-step explanation:

Given, x3+y3=(x+y)(x2−xy+y2)

First take R.H.S

(x+y)(x2−xy+y2)

To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial.

= x.x2−x2y+x.y2+y.x2−x.y2+y.y2

= x3−x2y+xy2+x2y−xy2+y3

= x3+y3

So, L.H.S = R.H.S

x3+y3=x3+y3

Hence, x3+y3=(x+y)(x2−xy+y2) is derived.

Answer 2

We know that,(x+y)³=(x³+y³)+3xy(x+y)

=>(x³+y³)=(x+y)³-3xy(x+y)

=(x+y)[(x+y)²-3xy]

=(x+y)(x²+y²-xy)