Question

Verify: x³+y³ =(x + y)(x² -xy +y²)​

Answer 1

$\huge \blue{heya \: mate}$

x³+y³= (x+y)(x²-xy+y²)

Now,

Here LHS= x³+y³

Now, we need to simplify the RHS

RHS:

(x+y)(x²-xy+y²)

= x(x²-xy+y²)+y(x²-xy+y²)

= x³-x²y+xy²+x²y-xy²+y³

Rearranging the like terms,

=x³+y³+xy²-xy²+x²y-x²y

= x³+y³

LHS= RHS

Hence verified.

Answer 2

$\bf \: x³+y³= (x+y)\bigg(x²-xy+y² \bigg)$

$\bf \: No,$

$\bf \: Here \: LHS= x³+y³$

$\bf \: Now, \: we \: need \: to \: simplify \: the \: RHS$

$\bf \: RHS:$

$\bf \: (x+y)(x²-xy+y²)$

$\bf \: = x(x²-xy+y²)+y(x²-xy+y²)$

$\bf \: = x³-x²y+xy²+x²y-xy²+y³$

$\bf \: Rearranging \: the \: like \: terms,$

$\bf \: = x³+y³+ \cancel{xy²}- \cancel{xy²}+ \cancel{x²y} + \cancel{x²y}$

$\bf \: = x³+y³$

$\bf \: LHS= RHS$

$\bf \: Hence \: verified.$