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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.

enter image description here

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1 Answer 1

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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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  • $\begingroup$ Thanks ! I failed to notice that ! $\endgroup$
    – Vince Vickler
    Commented Nov 13, 2021 at 13:13
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    $\begingroup$ @VinceVickler Without noticing that, you could still do it the hard way by considering the expression a quadratic in $x$, finding the roots using the usual quadratic formula, then factoring it. $\endgroup$
    – dxiv
    Commented Nov 13, 2021 at 19:54

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