TITLE: How to factor $ ab(x^2 +y^2) + xy (a^2 +b^2)$?
QUESTION [3 upvotes]: Source : poblem 291 ( image below)  of Lebossé & Hémery, Algèbre et Analyse  ( Classe de seconde , 1965)
Note : " classe de seconde " is $10^{\mathbb th}$ grade , which inspires me the reflection that I wouldn't have be admitted to  $11^{\mathbb th}$ grade in $1965$.
Developping I get ,
$abx^2+ ab y^2 + xy a^2 + xyb^2$
but I cannot see which known identity is hidden below this expression.
Symbolab is unable to give any answer regarding this factorization problem.

REPLY [5 votes]: Just notice that $abx^2 + aby^2 + xya^2 + xyb^2 = ax(bx + ay) + by(bx + ay) = (bx + ay)(ax+by)$
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