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4

MonomialList may provide functionality you're looking for here. P[x,y,z]=x y^2 z + 2x y z^2 + x^2 y^2; Q[x,y,z]=x^2 y z - x y z^2 + x^2 z^2; P[x,y,z]+a Q[x,y,z]//Expand will yield x^2 y^2 + a x^2 y z + x y^2 z + a x^2 z^2 + 2 x y z^2 - a x y z^2 Now, to get the factorization you're looking for, MonomialList[x^2 y^2 + a x^2 y z + x y^2 z + a x^2 z^2 + ...


4

Assuming[w > 0 && 1 > a > 0, Collect[(a w)^a (w - a w)^(1 - a), w, Simplify]] $\ $ (1 - a)^(1 - a) a^a w Simplify[Cancel[(a w)^a (w - a w)^(1 - a)], Assumptions -> w > 0 && 1 > a > 0] $\ $ -(-1 + a) (a/(1 - a))^a w Simplify[Together[(a w)^a (w - a w)^(1 - a)], Assumptions -> w > 0 && 1 > a ...


2

This is not a robust solution but since no one else was motivated to try to match your result here's my rough draft. expr1 = 225 a^4 + 600 a^3 b^2 + 520 a^2 b^4 + 160 a b^6 + 16 b^8 + 1200 a^4 b x + 2080 a^3 b^3 x + 960 a^2 b^5 x + 128 a b^7 x + 600 a^5 x^2 + 3120 a^4 b^2 x^2 + 2400 a^3 b^4 x^2 + 448 a^2 b^6 x^2 + 2080 a^5 b x^3 + 3200 a^4 b^3 x^3 + ...


2

e1 = 225 a^4 + 600 a^3 b^2 + 520 a^2 b^4 + 160 a b^6 + 16 b^8 + 1200 a^4 b x + 2080 a^3 b^3 x + 960 a^2 b^5 x + 128 a b^7 x + 600 a^5 x^2 + 3120 a^4 b^2 x^2 + 2400 a^3 b^4 x^2 + 448 a^2 b^6 x^2 + 2080 a^5 b x^3 + 3200 a^4 b^3 x^3 + 896 a^3 b^5 x^3 + 520 a^6 x^4 + 2400 a^5 b^2 x^4 + 1120 a^4 b^4 x^4 + 960 a^6 b x^5 + 896 a^5 b^3 x^5 + 160 ...


2

FullSimplify[] on the enormous expression gives this answer in less than a second: $(4 b^4 + 4 a^4 x^4 + 4 a b^2 (5 + 4 b x) + 4 a^3 x^2 (5 + 4 b x) + a^2 (15 + 8 b x (5 + 3 b x)))^2$ It would take me several days to calculate such a result "by hand," and no doubt I would make errors.



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