Question:
Find the product:
(x3 − y3) × (x2 + y2)
Solution:
By horizontal method:
$\left(x^{3}-y^{3}\right) \times\left(x^{2}+y^{2}\right)$
$=x^{3}\left(x^{2}+y^{2}\right)-y^{3}\left(x^{2}+y^{2}\right)$
$=x^{5}+x^{3} y^{2}-x^{2} y^{3}-y^{5}$
$=\left(x^{5}-y^{5}\right)+x^{2} y^{2}(x-y)$