Question

verify:x³+y³=(x+y)(x²_xy+y²)​

Answer 1

$\large\sf\underline{Given}$

• $\sf\:x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$

$\large\sf\underline{To}$

• Verify LHS = RHS .

$\large\sf\underline{Solution}$

$\sf\:Taking\:RHS$

$\sf⇾\:(x+y)(x^{2}-xy+y^{2})$

$\sf⇾\:x(x^{2}-xy+y^{2})+y(x^{2}-xy+y^{2})$

$\sf⇾\:x^{3}-x^{2}y+xy^{2}+x^{2}y-xy^{2}+y^{3}$

$\sf⇾\:x^{3}-x^{2}y+x^{2}y+xy^{2}-xy^{2}+y^{3}$

$\sf⇾\:x^{3}+y^{3}$

${\sf{{\blue{All\:the\:other\:terms\:gets\: cancelled.}}}}$

$\sf➤\:LHS$

$\small{\underline{\boxed{\mathrm\purple{Hence\: verified}}}}$

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